I did a site visit at the Sheraton on my last trip. Their club is absolutely amazing. Floor to ceiling diamond head views. It is also huge (as it was an old restaurant converted to the club). Everything was top notch in the club.

I've only stayed at the Sheraton once and it was a busier time so my Platinum upgrade was mediocre at best. However, you will likely have more luck with a paid stay vs mine which was a free weekend certificate stay.

IMO the beds at the Sheraton are more comfortable but the rooms are minimalist. They do have good views if you can get them and others in the SPG forum have reported getting them often. As I said, i think SPG in Hawaii treats awards stays differently than paid stays for upgrades so I was disappointed with my very partial ocean view room that was on the middle floors facing toward Ala Moana (so a view of the next hotel's balconies and when I turned my head I could see a bit of ocean).

The Hyatt also tends to be a bit noisy because of the Kalakaua traffic. The Sheraton is close enough to the ocean that you will likely hear the waves crashing at night if you can get ocean front. I know I could hear them from my 5th floor tower room at the Royal Hawaiian.

In the past I would have said Hyatt for sure. But after seeing that club, I honestly think Sheraton now has the best product going in Waikiki. As a Platinum you may not even want the breakfast rate unless it's the same because the club experience will be so good.

The Hyatt seems to be moving downward while other hotels are moving up. On a paid stay with top tier at SPG, I'd say go with them. On a reward stay I'd say go with Hyatt because I've always been treated well on award stays (as opposed to my average or below awards experience at SPG with the same level).