Just did a staycation with my wife and son for V-Day. Also wrote a parallel review of the Park Hyatt Seoul because our wedding anniversary is a week later, and I wanted to get some stay credits in before the end of February.
Amex FHR. Grand Hyatt made more of a deal about it, taking us to a special desk to check in even though the hotel was super crowded for V-Day. They are more generous with the stay credit -- ₩110,000 unrestricted, can use it for anything including room service. Overall, the first floor area with the restaurant feels quite "grand" in scale, and elegant in a somewhat old school way. The hotel didn't really do anything special in terms of welcome gift, however, no wine or anything waiting for us in our room, but we did get passes to the ice rink (but not free skate rentals). Not sure if literally everyone gets those passes.
I'd say the two main highlights of our stay were the ice rink and the food -- the food is really top notch. We tried both Korean and other Asian dishes -- really excellent quality for room service dining. We also bought a room for my wife's parents for the next night, and they also talked a lot about the quality of the food. Here I'd say Grand Hyatt beats out Park Hyatt though the ambience of the PH top floor restaurant is spectacular, I'd say the food quality was a step up at the Grand Hyatt.
For a staycation I think both of them have their advantages - the GH is more "fun", better dining, more flexible FHR credit, but the rooms weren't as luxurious and upscale/elegant in feel as the Park Hyatt, and the views were far less spectacular than the city view rooms at the Park Hyatt, and the rooms were smaller and more ordinary. On the other hand, because the PH is right next to Coex there are some excellent dining options there and we'll probably do a lunch or dinner at the department store across the street before we go home.