I haven't ever been on the beat per se, but I've been around it enough to have some ideas.
Among the pros: You've got a chance to build relationships with players and staff in a more intimate environment, which isn't really possible if you were to only cover the home games of an MLB team. Depending on the level - usually from High-A up - you could see some pretty good baseball; not that Low-A and short-season isn't, but I'll never forget watching an Aberdeen game a few years ago and marveling at the starting pitcher's 86-mph fastball (without the electric offspeed stuff). Assuming it's an affiliated team, you ought to have some interaction with the farm director of the big club. It's a different kind of beat, I've always thought, because the end result of the season - while important to some degree - isn't the explicit goal of a farm team. Wins and losses aren't the be all, end all; you're able to focus on development and keep tabs on how players grow (as Cosmo said, and I know that he knows of what he speaks).
Among the cons: In many places, the local minor-league team may only have one beat writer - you. So there's no external pressure to break news or do anything out of the ordinary, though hopefully that pressure is internal. Minor-league clubs, at least the ones I've dealt, have maybe one PR person who may have other duties besides that; there's no fleet of people like in the big leagues, so you'll have more legwork to do generally. You're working at smaller facilities that may not have space specifically for reporters; that's not the norm, though I know of at least one place out there like that.
That's off the top of my head, but it's a start...