I stayed at both hotels. The Park Hyatt is much smaller and more exclusive. A large selection of fabulous restaurants, (the earlier mentioned New York Grill is a must!) and very high, personalised service levels. Of course, prices to match...
The Century Hyatt is a larger hotel, but with all the facilities that you would need. Rates are quite a bit lower than those at the Park Hyatt, but the experience is very different too.
Both hotels are in Shinjuku-ku. The Park Hyatt is on the top floors of the Tokyo Gas Tower, the Century Hyatt is about three blocks away.
I would recommend either hotel. Take a look at the Hyatt website if you want to get a bit of a better idea.
www.hyatt.com or
www.parkhyatttokyo.com