I've stayed in all of 'em except Hilton St. Pete.
Embassy USF: Very nice ES. New property, usually very competitive rates. Do your Internet research, then call the property and see if they can beat the 'Net rate. They always have for me. They have a nice clean pool, high-speed data in the rooms, and all of the other usual ES stuff (cocktails, breakfast, etc.). Minutes from BG.
Embassy TPA: Older ES. Average for the chain. Customer service weak at this location; I was stuck in a smoking room when I had booked non, and I couldn't find a clerk who was both fluent in English and willing to help me out. Location is so-so - near the airport, but not near the stuff you want to visit. They have a pool, but I haven't spent time in it.
DoubleTree BG: I hate totally bagging on HHonors properties, but I thought this place was really, really bad. I had booked a 3-night stay there, and bailed after 1 night. Very LOUD hotel, outside corridors, very poor telecommunications system in the rooms. (Remember 14.4Kbps?? That's what you get here. If you are lucky.) This hotel routinely features rates under $70/night, so it probably attracts a different crowd than a usual DoubleTree. It does have a pool. Judging from the looks of the place, DoubleTree purchased the building from HoJo or something and fixed it up a bit.
I've also stayed at the Hilton TPA. Very clean, basic-service hotel. Not really a full-blown Hilton; more like an HGI. But nice and clean, and not too expensive.
Since you have kids, go for the ES-USF. You will enjoy it a lot, and there will be plenty of room for the little ones.