A giant is a completely different race to titans, they were born to be the gods opposites and fight them for control.
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Titan gods are one generation up and gave birth to the Olmypion gods. The Olympian gods overthrew the titan gods and began ruling the earth.
I wonder if you aren't confusing "giant" with "Titan". However, there was a less known battle between the Olympians and the Gigantes, giant children of Gaia. This war was known as the Gigantomachy, and the gods nearly lost, were it not for the timely intervention of Heracles. The giants were led by Alcyoneus and Porphyrion.
Hades is King of the Underworld, god of the dead - first born son of Cronus and Rhea. If by "counos" you might mean Cronus? Cronus is the Titan god of Time.
There are two goddesses that might be called the "goddess of reason:" Metis and Athene. There is a slight difference between the two. Metis is the Titan of wisdom and knowledge. Athene is the goddess of intelligence.
In Greek mythology, gods are typically more powerful than titans. Therefore, a god would likely win in a battle against a titan.