Coming from Hyperspin/RL setup, most important thing to me is startup fade - essentially, I want my machine to feel well oiled and no obvious operating system underneath!
Themability is key, and on RL I really love the fact that I can see System Playtime, Game Playtime, Number of times I've played the game etc on the fade in.
With Pause screens, it's all about controls and layout for me, followed by move lists. High scores would be good too, but absolutely not essential (and I'd need instructions on how to do it!)