I did it the other way around- I received a Starwood comp from my Hyatt Diamond status. After a few stays where I did not receive suite upgrades, I decided to stay with Hyatt.
Perhaps the biggest factor is that lately Hyatt has been adding benefits like the free breakfasts when there is no Regency Club. OTOH, Starwood seems to be trying to discourage members- no benefits if reservation booked thru Expedia[let alone on Priceline], more nights to qualify.
It seems to me Hyatt is trying much harder- I only hope they keep it up.