Why didn't they use the engine of Far Cry 2?
Several reasons.
1) Bethesda devs are/were far more familiar with the Gamebryo engine and what it can do and it's limits. By using a slightly upgraded version of Gamebryo, they cut down dev time between Oblivion and Fallout 3 and keeping the engine allowed Obsidian to focus on other elements when making New Vegas.
2)Switching to a new engine can increase development time immensly (ie: Look at Duke Nukem Forever, they changed engines everytime a new one came out and it's currently 12 years late)
3)Using someone else's engine can cost a lot of money. I've heard plenty of tales and stories about larger companies charging immense fees for another company to use their engine.
4) The Far Cry 2 engine is good at wide open spaces and combat, but on the other hand, apart from a single town and scattered collections of huts, it's reletively empty. It may not have been capable of the heavily detailed ruins of DC for example, even with the separate cells they used with Gamebryo. It may also not be up to the job of handling the heavy script use that Fallout 3 and New Vegas used.