A toss up. One study that directly compared 3 nasal steroids, including Nasonex (mometasone) and Flonase, suggests that Flonase may act more quickly than Nasonex (mometasone). However, research shows that the two are, in the long run, equally effective. Their molecules are very similar structurally & functionally. if you want to decide which one to use, base it on cost, convenience & comfort. Otherwise, it's a toss up!
Probably no differen. Although some (I believe Nasonex) are specifically indicated for nasal polyps, there is no real reason why the other won't work just as well although they have not been studied specifically for this indication. More important is the technique in using the spray and the total dose. Be sure to aim towards the outer direction.
Either. Depends on your response to either medication. Discuss with your ent doc.