I stayed at both the Mandarin Oriental (MO) and the Peninsula (P) in Nov2010, and both were great. If I had to choose I'd probably pick the MO if they were the same price. Here is how the different attributes stack up, in my opinion:
Location - P wins big, on the edge of the Imperial Gardens and Ginza. MO is a 20 min walk north from P.
Rooms - P. P had much beds, bathtub and toilets (an artform in Japan). MO had much better shower and toiletries (incredible products, esp the bathsalts). The decor and layout were equally wonderful at both hotels, as were the views.
Common Spaces - MO wins big. Though I am not a fan of the common MO setup of having the lobby on the top floor (requiring you to take two elevators from your room to the exit, one up to the lobby, another one down to the street), I loved the look and feel of this hotel - serene, lovely and efficient. Gorgeous views and architecture. P's setup is much more convenient, but the lobby feels small and chaotic with the restaurant planted right in the middle. Not a space where we wanted to linger in the least.
Service - MO wins big. P is fine, but MO goes above and beyond. The concierge staff at P was harried.
Food - MO wins. The food at the restaurant in P's lobby was mediocre. The food in the casual cafe in the P basement is tasty but the location in the basement in not ideal. We didn't try "Peter", on the top floor of P, because the cigarette smoke was so strong.
MO has five restaurants - four with incredible views, (including the all-day dining, more casual place which had a wonderful breakfast buffet) , three with Michelin stars.
Gym - tie. P has a lovely pool, but the gym is small with no windows. MO's gym is bigger with great views, but no pool. Both had nice, new machines.
Spa - P because of pricing. MO's is egregious, even for Tokyo.