I have been staying there several nights each year since the 1990s, and I echo what others have been saying about this differences being negligible. My gut feeling is that Shinjuku view = your primary view will be Tokyo Metropolitan Government Bldgs and their grounds. City view = most rooms to your left (as you exit the elevator bank) w/o direct views of the Tokyo Metro Govt Bldg. Either way, you will see the city skyline w/ similar sets of highrise bldgs.

I may have it backwards, but the differences are pretty much unnoticeable (which is probably why I can't even remember for sure which is which). Sure, the Tokyo Metro Govt Bldg is an icon, but it's not like it's pretty to look at or anything...