It's partly history. The Gibson company had scroll models in both their mandolin and guitar lines, mostly for show. But when Lloyd Loar designed the F-5 mandolin, he used the fancy F-shape as the starting point, then did his "copy a violin even more than earlier models" experimenting. The result was a loud, very playable instrument with a distinctive tone. A deal of the tone comes from the f-holes instead of the oval sound hole of the earlier F- and A-models. So you could get an F- model with an oval soundhole, or an F-model with f-holes.
The difference, structurally, is that f-hole instruments don't have this honking big hole in the top between the bridge and neck, a hole which has to be reinforced against collapse. For this reason, A-models have either braces or a thicker top around the area of the soundhole, which cuts the volume but gives you more sustain and a little 'sweeter' tone. Most old A-models are sweet but silent (comparitively -- no good mando is 'silent'). F-models are sharper and woody in tone, and tend to be louder with less sustain.
All of these comparisons, of course, vary from instrument to instrument -- my A-model Gibson is louder than my "Loar" F-5, and the Mid-Missouri flat-top is probably louder than the Gibby.
So it comes down to the individual taste and style of music you're after playing. For string-bands, A's work well enough. In a bluegrass band, at full roar, you may need an F, and maybe even then, a pickup. For parlor music, go for the sweet, and as much volume as you can get among the sweeties. Try lots of mandos, side-by-side if you can, and expect buyer's remorse no matter what you get. I liked my "Loar" just fine till I sat in with folks playing REAL Loar mandolins, and then it sounded wimpy and thin. But then, against a real Loar (1921-1925 are the production years) nothing else has both the quality and the aging that produces a real killer instrument. You're getting into the "what will my modern instrument sound like in 50 years of playing?" territory, which is another subject entirely.
If I had to go looking for a new mandolin, without my current ones to 'fall back on,' I'd probably check out Eastman, "The Loar," plus Webber, Breedlove, and some of the one-man shops, and probably look for an A model -- maybe even an A with F-holes (Gibson A-40 or A-50 models from the 40s are like that).
And, no, the scroll doesn't affect the sound a whole lot, one way or another. It's just a chunk of wood glued to one side, and not much involved in the vibrating part of the instrument. The neck has more to do with the sound than the scroll.