We always use TPA when going to Florida, and although the prime reason is location [we holiday on the Gulf Coast] I would choose it every time over Miami even if it meant an overnight hotel stay, due entirely to the speed through immigration.
The BA flight from LGW is the only international arrival in late afternoon, and when we arrived on Feb 5th [still in Florida as I write] we were through immigration less than 30 minutes after the aircraft touched down. Admittedly we were relatively near the front of the cabin [in WT], but even so, a good performance. Also, staff were all polite and friendly.
The only downside is the design of the departure area - the limited number of restaurants and stores are all in the central departure area, and once you pass through the security area for each satellite, there are no other facilities.