fluoro is supposedly more "invisible" underwater, and people thinks it makes a difference. I personally don't believe this, but to each thier own.
It's also a smaller diameter than mono, so a 15# diameter, it basically equivalent to that of 12# mono... so you can throw a higher weighted line and not lose the diameter.
Fluoro also is heavier, so it will sink faster - good if you are a texas rig fisher and want to keep your baits on the bottom... I use a lighter jig weight than most people too - so a 1/4oz that people throw with mono, is almost the same as me throwing a 3/16oz with 15# mono... and it does fall a little slower.
Next is crankbait fishing... if your lure says it will dive 9-12', that's pretty much based on 10# mono line. I don't throw line that small, and if you throw that lure on 12# mono, it will run pretty much 9'. I throw that same lure on a 15# fluoro and I actually achieve 12' with a good Medium action rod and a looong cast. You can pretty much figure 6"-1' more depth when running on fluoro. So that same 9-12' depth crankbait will run closer to 10-13' on a 10# fluoro line.
It's more abrasion resistent than mono (in some instances) and the knot strength is sometimes better, but that depends on the brand that you are using.