I usually go for House. NCR are a bunch of murderous hypocrites, and their taxes which make no sense. Caesar's Legion is at the height of power in their history, but Caesar unknowingly has become like Tandi. Which means once he dies Caesar's Legion won't die, but it will change until it is no longer Caesar's Legion. Once they reach sustainable prosperity in their territory. Caesar is even planning on turning them into a praetorian guard to defend citizens. Once Caesar's Legion loses that edge? It will become malleable, and through a combination of indoctrination and reeducation, their empire will become weak. They will become the NCR. Good times foster weak men. As the saying goes. It's their poor condition prior to their rise to power that made them strong. Once they win? It's all downhill from there. It might take a couple centuries, but it was not built to last.
Now with House, besides being less morally bankrupt than either the NCR or CL, he has a game plan that works. He has the pseudo-immortality to make sure that plan stays on track, and he has you if he dies. Who will have access to that same technology. An army of robots that don't need to eat or drink, and which are self-repairing. A way to bring in revenue thanks to his casinos. His reach which extends across the Mojave, and his ability to negotiate with pretty much any faction. Only exception being the Brotherhood of Steel.
Once the NCR and Caesar's Legion collapses? I imagine he will then enter into an alliance with the Brahmin Barons. Unlike the NCR? House knows their game, and won't let them exploit him. Instead he will enforce actual equivalent exchange in their contract, and won't allow them to have too much power or influence in his territories. He will take what he needs from them, and keep them on a tight lease.