I don't know if the new client is coded specifically for 60fps in mind, but from my current experimentation with the current client's framerate control it's a bit sloppy. Basically you have to code your server from scratch to anticipate different framerates. For example, the lowest timeout currently is 0.05 because 1 second/20fps = 0.05 seconds. Pretty much every script uses 0.05 timeouts. They won't break, but you won't be getting the full potential of >20fps. 1/60 = ~.017 which would be the new lowest timeout. So everything would have to be coded from the ground up in anticipation of this timeout. However... as far as I know Flash doesn't support >20fps, their new client might though. So 0.017 timeouts aren't going to work for Flash users, but it won't break. It will default to 0.05, but anything based on timing will break. Also, ganis assume 20fps, so 60fps increases gani animations and default movement. I don't know if they also recoded default movement, but if you plan to use a new fps you're gonna need to code your own movement and anistep handling so it animates properly for different framerates. Also none of the default functionality that is determined via time will function correctly, for example anything using move() will glitch out with a framerate > 20fps as they move faster than anticipated and the server snaps them back to where they should have been.
Like I said though I haven't tried this new client so I don't know if they have fixed all of these things, but >20fps is only viable if you plan on building a server from the ground up to actually support it to its fullest potential. I also don't know if they've changed how it's implemented. Currently you don't define the desired FPS... it uses some weird inverse scaling value.
Also, 60fps isn't going to magically make things run better. If you're getting 10fps because of performance issues you're still going to get 10fps even if the server tells you to run at 60fps.