Pro Tools has a more traditional DAW workflow and is very much a standard with people that has to mix big projects (50-200 tracks to pick a number) due to their excellent but expensive cards (HDX now).
FL Studio has somewhat of a special workflow derived from the early Fruityloops versions that was operated pretty much like a stepsequencer. FL has grown though into a complete DAW made lately fameous by house prodigy AVICII and many others. AVICHII still sticks with FL Studio. And he does it really well.
And yeah, a lot of people use PT for mixing while doing their creative work on a different DAW. But keep in mind that many of those has hardware accelration cards in their putters from AVID (PT maker) that makes PT a much better platform for mixing and end production. Protools also have great workflow for working specially on audio files wich most final mixes comes down to.
Suggestion; download them both and try them.
To help you further I have some questions.
How is your experience in music production?
What music are you about to make (or are you gonna mix others work)?
What is your budget?
If you are on a low budget and e.g. already owns a mac I would say nothing beats Logic in the bang for bucks-division.
Well, can tell you a lot more but need to know more about you, your goals, budget and plans.