If you don't get any responses or adequate answers to this question, it may be due in part to the fact that this sort of information would be considered a spoiler. KingsIsle wants you to go and play through their game content and learn for yourself what there is to learn, and experience..blahblah okay you get the point.
For a more direct answer, I'd suggest visiting one of the W101 fansites, if you haven't already done so or battled through the tower. My suggestion? wizard101 central. Never lets me down and I've learned more than any tutorial tip in-game could ever wish to provide.
Besides badge, Briskbreeze has possible drop of good ring and athame of each school, currently the best are in Helephant tower or crafting based on POV. Good luck, at moment Briskbreeze is old news for farming.
The Briskbreeze quest itself gives, unfortunately, very low xp, even for a level fifty wizard (I think it's somewhere in the 200's?). The battles themselves could potentially give a lot of xp, but if you're a balance like myself and you're being constantly asked to buff (0 pip balanceblade, anyone?) then the amount of xp you get is limited. On the topic of the equipment, for the first several monsters, you get standard mob drops, mostly level fifty and up gear as I recall, which can be sold for several thousand gold. The boss on the fifth floor (or is it the sixth?) may drop something good, but that was one of the battles where I did not use one attack spell, so I got no equipment drops from this. The final boss, however, has grandmaster school-specific no trade no auction ring drops (quite a mouthful, right?). So unless you're willing to farm Briskbreeze multiple times for your school's ring, or you get lucky on your first shot, you get a 100% useless hunk of unwearable virtual metal, which barely sells for anything since it's no auction and can not be placed in the shared bank because it's no trade. All in all, Briskbreeze has very few rewards considering the time it takes to complete it. The only worthwhile thing that I received from the tower was the badge.