Of course, people's opinions on whether there are "much nicer hotels in Tokyo for the same price" do vary!
Diamonds also get free access to the sauna and associated stuff, normally costing Y4,000 extra.
I agree you should compare the Amex FHR rate to the website and any other discounts you might be eligible for.
Rooms go: Park, park deluxe, corner king (or some name like that), park suite, and then bigger suites. I prefer the park deluxe to the corner king, but others disagree here too! Park rooms, the lowest grade, come as a park double or park king, both typically at the same price -- but the park double is larger.
The 'small' park king referred to above is larger than virtually any room in any non-deluxe hotel in Tokyo.