Have gone February and September many, many times (see signature!)
February...generally dry season, generally warm. That said: this year was a big exception. Had both colder than normal and warmer than normal (in the same week!) Also this has been a very wet January & February for Florida. So that must be considered a possibility. It is major ride refurbishment time, though, and water rides will often either be down for painting, etc. OR they are closed because it's too cold. Also often too cold to swim in resort pools. Crowds can be extremely low. For example, we were at WDW this past week, Saturday 2/8 until Wednesday evening 2/12. Went to all 4 parks...DHS, Epcot & Animal Kingdom probably about a "2" on the crowd size. MK on Wednesday maybe a "3". OUTSTANDING.
September...still FULL SUMMER in Florida (highs in the 90s, with extremely high humidity), and it is prime hurricane season, too (that's where all the rain comes from: it is the storm season in Florida) It is completely possible your vacation can be wrecked by tropical storms/hurricanes/tornadoes in September, so keep that in mind. The summer storms in September can wreak havoc on transportation (major flight cancellations are possible, and not just in Florida, but all the "connector" hubs for major airlines too.) So your flights could get cancelled. (Though the same is true for flying in February, as this year has shown...1000s of flights cancelled due to crazy winter weather.)
But...September usually has the lowest hotel rates and the best discounts (that's when the original free-dining discounts started...to bring patrons in during hurricane season) The crowds can be remarkable empty in September. Labor Day weekend can have crowds, especially at Magic Kingdom (popular with locals) But the week after Labor Day can be crowd size 1s and 2s. If you go 2nd week of September you can get tickets for Halloween party and will find it is small crowds for Halloween party.
I would say...if you don't mind hot, and you want to swim at resort, do water attractions and maybe a water park then go in September.
If you don't do heat/humidity, don't care about swimming & water rides...then go sometime during the last week of January (Not MLK Jr. holiday weekend, the week after that) or the first two weeks of February (leave before Prez Day weekend) The rates will be almost as low as September, and can have great low crowds.