The big advantage zone gives you (IMO) is flexibility. You have flexibility in team construction on a couple different fronts, that have been mentioned by others. Since I play HCP with zone, I don't get to take advantage of the multiple walk-on strategy, but it's there if you go straight zone. But you also have the flexibility to go after guys with elite skills who may have "flaws" that can keep other teams off, and let you get them for relatively cheap. Zone is well-suited to recruit and utilize role players. A guy with exceptional point skills can thrive on offense, and be paired with a stopper at the 2 (or 3 in a 3-2) on defense, and it won't kill you. Likewise, a 5 with extreme Reb/Blk ratings but sub-par def can still be a defensive asset down low.
From a gameplanning standpoint, you also have a lot of options. If you expect your opponent to pound the low post, you can run your best 3 Reb/blk guys at 3-5 in a 2-3. If you expect him to go bombs away, you can load up on perimeter D with a 3 guard set in the 3-2. You can still cheat at -1 or -2 in a 3-2, and effectively defend the perimeter against most teams, while giving your 2 low post defenders a head start in rebounding. In a perfect world, I have a swing who can handle the 3 in both sets. In reality, I usually lean heavily one way or the other for most of the season, based on what I think my best lineup is. But theoretically, playing a zone can give you a level of unpredictability in tournament time.