Focusing on the opposing generals is always a serious oversimplification, IMO. Western generals were much farther away from Washington and could get away with a lot more mistakes, allowing for men like Grant and Sherman to learn by trial and error how to fight a modern war and ultimately become the Union's best generals through experience gained. In the east, it's not three strikes and you're out, it's one strike regardless of whether Lee is your opponent or not. Had Grant somehow made his way to command the AoP in 1862-1863 we can at the very least reasonably assume that he wouldn't have lost his nerve in a major battle and would have put all his men in, and no one can really say what the outcome of that would have been since there's no way to really set up a hypothetical battle like that.
Unfortunately I can't really agree with any of the poll options, personally. My answer would of course be more along the lines of, "Yes, because the political pressure wasn't nearly as strong on the western army commanders."