Not sure if this is still relevant given the question was asked three months ago, but FWIW, I would prefer the MS over the Palm
1. I don't like the pools at the W Palm. The layout is weird and the one with the bar can get super crowded. The collection of pools at the MS is far superior IMO.
2. The beach is slightly nicer at the W Palm though
3. There's more F&B options at the MS as you can walk over to eat at the outlets in Westin and LM (Italian, Thai, French, Steakhouse, Greek etc.) and charge to your room whereas at the W you're stuck with a handful onsite options which weren't that great (Sobe has a good vibe at sundown though)
4. At the W MS if you wanna venture out, there's a tram just outside the hotel which can take you to JBR, Dubai Marina etc.. for several dirhams whereas at the Palm you're stuck with Taxis or Ubers/Careems
5. The hard product in both hotels are very nice. If you can score higher category suites at the W Palm you will be stunned. Not so much at the W MS - whilst the suites are nice, the ones at the Palm are just MASSIVE and is at another level (they're designed for in room parties)

All in all, the W Palm has better rooms if you can score higher category suites (e.g., using SNAs) otherwise the W MS wins in just about every other aspect that matters to me. W MS also feels more intimate whereas the W Palm can feel crowded especially during weekends when they sell pool party accesses. AFAIK there's no such thing at the W MS (yet)