I just stayed at both PdG and Park Hyatt last week.

The hotels definitely have a different feel. Park Hyatt seems to have a dark more luxurious vibe, but upgrades (even for a Globalist) will probably be difficult and you will probably be stuck in a fairly small standard King Room that still feels very luxurious with a smaller bedroom area, and a large bathroom. Breakfast service was a bit better at the Park Hyatt than the PdG in terms of quality of food and overall attentiveness.

PdG rooms are decorated more in an art deco style which is interesting, but to me doesn't scream luxury, but the Macassar suite we were upgraded to last time was truly amazing, and the service was top notch. Assuming you have Platinum or better status, at PdG I believe you would have a much higher chance of an upgrade to a much more spacious suite.

If I had no status in either program, and rates were the comparable I would go with the Park Hyatt vs. PdG.