Two very different areas. I am just north of Naples, moving to Naples in about 3 weeks. I have family in Sarasota. Other than shooting, what other hobbies and things you enjoy doing? Do you like nightlife or more relaxed evenings? If you are set on Hillsborough for your job, then Sarasota. HC is about 2 HRS from my area. Sarasota is very artsy area, tons to do, good nightlife.....there is a lot more tourism in Sarasota with Siesta Key and St. Armand's circle right there. Naples area has a good amount to do as well, more relaxed area. There was just an article about rents in Lee & Collier counties, it is averaging in the $2k neighborhood depending on area, size, amenities, etc...
As far as shooting, there are more outdoor ranges towards the Sarasota area, having said that, from June to October I wouldn't want to shoot outside unless you are there when they open and shoot for a few hours.
Shoot me a pm if you gave any questions. I've lived here for 12 yrs and have seen the changes to my area.