Generally a parliamentary form of Government is a democratically elected form of Government (although there are exceptions to this, for example, once Hitler had been elected to power in Germany he retained the Reichstag, but effectively barred free elections).
Democratically elected Governments can be viewed as being representative of the people and therefore less likely to be extreme in nature or to exact cruelty on their electorate. In short they will protect and attempt to enhance the quality of like for those who voted them in.
However, there can be disadvantages as well. Democratically elected Governments may be unwilling to address some of the trickier questions or harder issues, for fear that if they raise taxes too high or cause major inconvenience to some of the electorate, they will not be voted in again.
Thus parliamentary forms of Government may be viewed as flawed, but perhaps they are a safer option than a dictator or supreme ruler.
AnswerAs the question involves two different forms of government for a representative Democracy, I think we can dispense with the justifications of the democratic form of political system.
This is a difficult question to fully answer, as much depends on the actual details of how a parliamentary or presidential system is put into practice. However, I'll try to outline the possible benefits and pitfalls of each system, though a particular implementation may not have any particular benefit/weakness, due to the details of the system.
Parliamentary SystemsAdvantages:
- The Executive leadership always reflects the current"will of the people" - that is, the Executive branch must maintain sufficient popularity at all times so as to satisfy at least a bare majority of the people (via their parliamentary representatives)
- The Executive is divided into functional groupings, and each Ministry has a head directly responsible to the Legislature, NOT to the Chief Executive. Thus, Ministries are head more closely accountable.
- The Executive, composed of multiple Ministry heads, plus the Chief Executive, can contain many diverse interests, or at least is not controlled by a single political party. There is thus a significant inherent "check-and-balance" in the form that competing interests will attempt to keep other interests from exerting too much influence in the Executive
- Elections to the Legislature are not at fixed intervals, and thus, the people can force a reconstitution of the government if it should fall too far out of popularity
- ALL posts in an election are up for grabs. There is no concept of independently-determined length of terms.
- Due to the requirement to maintain a Parliamentary majority (or, at least, avoid a vote of No Confidence), the Chief Executive's foreign policy will be assured of sufficient backing to put in place any negotiated treaties, et al. that the Chief Executive works out with any foreign power. That is, it gives foreign powers the confidence that the Chief Executive speaks with absolute authority (and can guaranty results) when promising provisions of treaties.
- The normal nature of Parliamentary elections results in a diverse set of Political Parties - typically numbering at least 5.
- Political Parties tend to be issue-based. That is, a Political Party's strength is tied to its position on a relatively small range of specific issues; the relative power of that party is thus directly related to the popularity of that set of stances on issues.
- Political Parties are much more likely to die when their fundamental issues fall out of favor; conversely, starting a new party is much more possible than under a Presidential system
- Parliamentary systems allow for modest minorities to form blocks and gain some minimum level of voice in government.
- As governments are almost always the result of coalitions of parties, they tend to be diverse and represent a wide swath of popular opinion
- As the Legislative and Executive Branches are closely linked, there are far fewer contentious problems between them; particularly, funding and ministerial direction tend to be much more closely aligned with Legislative priorities
- Voting tends to be more party-based, and collective in nature, allowing for more useful voting strategies by individual voters, which tends to produce elected officials more in tune with a larger majority of voters.
Disadvantages:
- There is little check on a demagogue's power should that leader be able to assemble a single-party majority.
- Minimum levels of vote accumulation set for Parliamentary representation means that actual Legislative makeup is not directly proportional to the popular vote. That is, by setting a minimum vote requirement (often 5-10%) for a party to receive ANY Parliamentary representatives, it shifts power to those with the most popular ideas away from those with small constituencies.
- To go along with this, there is very little incentive for the larger parties to pay any attention to the very small parties issues. Thus, small opinions go unheard or ignored.
- However, there is a related problem. In systems where there are a large number of parties, and very few parties can consistently pull even a large minority of votes, the government requires a broad coalition. The practical result is that small parties (those with enough votes to get Parliamentary representation, but not very many) wield a very outsized power, as such coalitions require consensus on ALL issues in order to remain in power. This leads to very unstable or inept government, as it is, by definition, Government By The Lowest Common Denominator.
- Inter-ministry competition (or friction) reduces the efficiency of the Executive.
- The direct tie between the Executive and Legislative branches means there is effectively no check on either's power by the other.
- The Executive is required to maintain a constant majority in the Legislature, which limits the ability to take short-term unpopular decisions (this can be an advantage, but also hamstrings the ability to make beneficial longer-term decisions which have unpopular short-term effects).
- Many Parliamentary systems still have monarchical ties, and many still contain significant autocratic privilege. This, of course, is most pronounced in the Constitutional Monarchy form of Parliamentary government, but is also present in many (nominally) pure democratic parliamentary systems.
- As terms in office are not fixed (typically, there is a maximum amount of time set between elections, but it can quite substantial), a popular government can stay in power for a significant time without having to be subject to elections. In a related note, since elections are called by the Executive, they can be gamed to be held during periods of maximum popularity for the current administration. Overall, failure to have regularly-scheduled elections allows for significant gaming of the system by all parties, both in and out of power.
Presidential SystemAdvantages:
- The Executive is fully self-contained. That is, all portions of the Executive report into the Chief Executive. This leads to a far more cohesive (and nominally, more efficient/effective) Executive branch, as it eliminates many of the inter-department competition and friction points.
- The Executive has a fixed term to serve; this puts a maximum limit on their time in office (even more so, if a maximum limit on the number of terms is enforced), preventing extreme stretches of single-person rule
- Within that fixed term, the Executive does not have to worry about popular opinion (or, at least, they cannot lose their job if their popularity sinks below 50%). The Executive is thus able to have a longer-term view of policy, given that they are not constrained by immediate effects of that policy.
- The prior point is particularly relevant for the Chief Executive's role as military leader. Generally speaking, it allows for Presidential systems to conduct military operations using long-term strategy.
- There are significant checks and balances between ALL branches of government, preventing one branch from exercising too much power.
- The Legislative branch has fixed terms for all members, though the length of those terms may not all be the same, and indeed, may be different than that of the Chief Executive. This leads to (relatively) frequent elections, which means the people are being frequently asked their opinion of those in power.
- However, within those terms, both the Legislative and Executive branches have more freedom of action (for both good and ill), since they know what their (minimum) time in office will be.
- The nature and design of elections typically means that Presidential systems have two main parties, with some also having a substantial minority 3rd party. As positions are typically won on a pure plurality basis, political parties are interested in appealing to the widest group possible. Political parties tend to be long-term, with very few new ones being created (and established ones very seldom dying).
- On a similar note, minority opinions are absorbed into one of the few large parties, as individual votes matter in the quest for a plurality. There are fewer choices in terms of party, but each party tends to represent a larger swath of the populace.
- As parties are required to produce a plurality for ANY representative, they tend to eschew radical positions (that is, ones which have only a very small following, but which are anathema to much larger swaths of the populace).
Disadvantages:
- Isolation of the Executive branch from direct popular opinion makes is possible for the Executive to implement very unpopular policies that cannot be challenged for quite some time.
- Similarly, it allows the Executive (possibly) too much freedom in military operations, particularly in the arena of short-term military adventurism.
- Fixed-term positions in both Legislative and Executive branches can allow for power-base building, making it hard to break established party control.
- Legislative districts are typically single-representative only, which leads to some bad electoral behavior, in that substantial minorities can be ignored if a representative has a stable majority (it doesn't have to be a solid majority, it just has to be a 51% majority that is loyal).
- There can be very substantial Executive/Legislative friction, and even inter-Legislative friction, as the system allows for each group to be independently selected, and this can mean very different groups control different sections of government. This can lead to extremely inefficient governance, as all inter-governmental actions are gridlocked.
- Elections are for individuals, though party affiliation can matter significantly. This allows for demagogues to build power bases far easier than in a Parliamentary system, where a person must have both enough popular votes for their party to gain a seat, AND must be popular enough INSIDE the party to be appointed to that seat.
- Parties are fairly static, which can lead to significant ossification and over-concentration of power inside those parties. It also means that politics is mostly dominated by very large blocks of ideology competing, with much of the subtlety of individual policies being ignored in favor of huge sweeping (and inaccurate) ideological statements.
As I mentioned above, the Devil is very much in the Details.