If it's between the 3... it really comes down to preference.

Service/amenities: Grand Hyatt and Park hyatt are quite comparable. Both are high end Hyatt properties in Tokyo. the Regency is not considered high end, so you will see a dip in service compared to the GH and PH. But, still a nice property. Especially for the amount of GP points required to stay there (if you're considering an award stay).

Location: This is what usually divides people. The regency and the PH are in Shinjyuku and are somewhat close to each other. The HR can be accessed by train much easier than the PH since the HR is pretty much connected to the station. The PH might have a bit more of a walk. But, Shinjyuku isn't exactly bustling with nightlife if that's your thing; but if you prefer less nightlife, then go with the PH/ HR. The GH is in Roppongi and is connected to Roppongi Hills. Plenty of things to do in the area, and is a hub for foreigners in Tokyo. Shinjyuku= business area, Roppongi= nightlife.

Honestly, you if you are considering all 3 equally and have the funds (or points) to do so, I'd eliminate the HR altogether since the PH and the GH are both a blast. It just comes down to what you are looking for outside of the hotel, in my opinion. Also, just my opinion but I felt like the GH was more of the sleek and bit more modern property while the PH was the classy, property.

If it means anything to you, I did see the GH on the top 500 hotels list and did not see the PH there.