I've had several holidays in both Florida and California as well as in other places in the US.
A few thoughts:
Firstly the weather. Florida will still be hot in September and October but California may not be. I personally love the summer weather in California but have never been in October. Maybe others can advise. You are in the hurricane season in Florida at that time of year. Chances are you will be fine but I wouldn't risk it having already had a holiday ruined by a hurricane.
The shopping in both is brilliant.
The beaches in both are lovely but I particularly liked the beaches on the southern golf coast of Florida.
The theme parks in both areas are fab (if you like that sort of thing). I preferred the California theme parks, particularly 6 Flags Magic Mountain.
I am not a golfer but there seems to be great golf in both places. We had a few days in Palm Springs, an easy drive south of LA, and the golf courses there looked good. A 2-centre trip with a few days in LA nad a few in Palm Springs might suit.
Florida is much more touristy. You keep bumping into other Brits. We enjoyed meeting people far more in California.