With Fallout 4 making an impact...
I tried to play New Vegas again recently but I only got a few hours in before ending up feeling that putting up with the mouse controls was more effort than it was worth. The problem is Vsync. Vsync delays rendering frames until they sync with your monitor's refresh rate, which causes the perception of lag on your input. I don't know why this is a problem when a simple frame limiter (e.g. fps_max in Source engine games) works fine, but I would guess that a frame limiter puts the game to sleep so it discards your input and therefore only responds to up to date mouse/keyboard events, whereas vsync lets the game run as normal but it delays rendering frames, so the display on your screen is slightly out of date.
Anyway, the point is that it feels awful enough that I don't play games which force vsync. Skyrim was exactly the same, but with the added bonus that if you hacked vsync to be off, the frame rate increased and the physics engine couldn't deal with it. Tying game speed to frame rate is extraordinary in 2015 in that it's so obviously wrong and not very difficult to implement correctly.
According to this thread on Reddit, Fallout 4 has the same problem, which is a shame but not really a surprise.