We've stayed at all of them and personally love the Thompson for the rooms and rooftop but probably prefer the Grand for the pool, fitness center and they have a great rooftop as well.

Here's our review of the Grand Hyatt Nashville: https://www.liveluxetravelco.com/blog/grand-hyatt-nashville-review

Both have 3rd night free offers through Prive if you end up booking a cash rate. If you book with points, Grand Hyatt is a little better value as it is a Cat 5 vs the Thompson which is a Cat 6.