I can see MS totally improving the load times to get into achievements, since they've been updating practically everything about the system on a month basis. It's safe to assume now that the OS will only get better and better with more features and tweaks every month. Like @bigjeffrey above me says, next month will add snapping of achievements so you can follow them directly and actually have progress trackers. Really neat, I think.
It's still not near as bad as the PS3 XMB though. Man that takes ridiculously long to get into trophies. I actually haven't tried it yet on the PS4.
Oh my God, yes. Anybody who thinks either the One or PS4 are slow need to take another look at the XMB. One time it took a whole five minutes to open up my Trophies menu and get all the games to load.
Trophies sync in a couple seconds on the PS4.