Which makes more sense for 65 yr olds?

Depends on what part of florida?
check out Perdido key , FLa just west of pensacola. They get alot of snow birds. It seems to me that if you plan to stay several months... 3 months or more at a time you should buy and then maybe have an agent rent it out during the summer. Check out Sea spray condos in perdido key.

If you are still in the 'looking to see where we want to be every winter', then I think it would be best to rent for a season or two, until you find the right area. Then you can decide whether you want to invest in a second home/condo.
Are you certain you want a condo? Would a small house be better, or even a mobile home park (there are some very nice ones around)?
What are the monthly fees compared to renting? Also in Florida if you rent for less than 6 months there is a short term rental tax...sorry forget how much per month, but it adds up. Also if you buy, you will have the monthly utility bills to consider...although with things like the telephone and paper & cable you can have them put on 'vacation' too and only pay the minimal or no fee except to start up again.
We rented a house two winters ago and enjoyed the yard, our own pool and the room. Last year we rented a duplex condo while our house was being built. My husband didn't like the condo because he didn't have his yard to putter around in...and we are not golfers.
Just some things to think about. We live in SW FL about half an hour from Ft. Myers.

My parents spend two months every winter on Anna Maria island in a rental condo. They are now closing in on age 80 and began going there in their late 60's. They passed up a chance to buy a 2 BR / 1.5 bath condo ten years ago because my mom thought the price was unreasonable for the condition (it was $65K but needed a new kitchen, bathroom, carpeting etc.). They now kick themselves for not buying. Units in that building in good condition are now selling for $135 - $150 K. There was a glut of units for sale and a depressed market in FL condos in the 80's but that seems to be gone. In addition to kicking themselves for not buying when they could (it's now out of their price range), they have difficulty rentring for two months. All the owners who rent out units want folks for three months or longer. They are currently paying $2200 per month in the winter and scrambling to find places on the island. If your long term plans really do focus on parking tyourselves in one place every winter it makes sense to buy but I would rent for the first two seasons to be sure it really suits you.

Any good financial advisor would ask a million questions before answering yours: tax situation, worki situation, etc.

However, the "rent first, then buy" is generally good advice. Or else you could end up making a good real estate investment in a place you hate.

As for personal experience, we had been visiting the Melbourne Beach area for years, and liked it a lot. So we finally bought a townhouse there that we use part of the time and rent out part of the time. I'm in a job where I can work offsite so going to FL for a while is no problem.

I guess if you want a really informed answer, you'll have to ask me in five years.

I live in Wisconsin, a very "tax-happy" state. Many retirees here purchase a second home in FL and then stay there just over 6 months of the year in order to declare FL their home state for tax purposes. You should consult a tax advisor/lawyer and, as previously stated, if you don't know where in FL you would like to be rent and do a lot of searching. Maybe by the end of your first winter you will know what you want to do.

I'm leaning towards just renting. We've spent a lot of time in Florida but through the years (we're also in our 60's) have found it to be really over rated. To escape the cold weather, we've found California and Arizona to be more to our liking. I'd encourage you to rent first.

My parents retired about 30 years ago to Cape Coral, Florida. They knew they wanted to retire to Florida, but thought they'd follow friends' advice and rent a mobile home to see if they liked it -- they didn't and finally bought a very modest new home. They had a very limited budget and income. After about 14 years and after my dad had passed away, Mom sold the house and moved to a condo (I bought it and she helped pay the expenses as rent). The money she made on selling the house is now providing her with enough income to live fairly comfortably in an assisted living facility (she is now legally blind among other problems, but has a good mind and still gets around and enjoys life). If they had originally started renting instead of buying that house (when does real estate not go up in Florida?), I'm not sure how she could be living the way she does now.

Sometimes retirees worry about the investment or expenditure of their funds as it relates to leaving it to their kids. A more relative question is how it might affect their long term living arrangements. Buying property to live in, in Florida (selectively) usually should prove to be a better investment than renting -- especially if only in the very expensive "season".