House wants to keep New Vegas just as it is. Him raking in all the money from Casions while the outside areas like Freeside are left to their own. The major problem with this is that House is an egotistical asshat.
The Independent New Vegas path is basically just that. Free of House's money mongering. With no masters that are either far away or sealed up tight, they are free to prosper on their own.
NCR's interest in the citizens of New Vegas really seems like a front to me, they want the Dam most of all, but if they spread their democracy to the Mojave that's just a positive anecdote. Then again, it's a really heavily bureaucratic democracy.
Caesar's Legion seems to be all about unity. Even though they practice slavery and sixism, Caesar took groups of loincloth-wearing tribals, ended their wars with each other, and educated them. What's interesting about Caesar's grab for the Dam is that his faction shuns technology, so it's possible the wealth of Vegas is what they're after rather than the Dam's power.