Fast, I don't see the difference between divisions and handicapping???
There is a difference. There are two situations really: inter-club tournament seasons and local tournaments in a single pool hall.
For the season, players from each club are known and registered in several divisions. For instance, I'm in division 1. Above me, there's the honor division, below me there's divisions 2, 3, and 4. During the season, my team can only play against division 1 teams from other clubs. I don't get to play against honor, 2, 3, or 4 division players. So we evolve in our little sub-group of similarly skilled players, while better players play against each others, weaker players do the same. At the end of the season, if we're ranked in the 3 first spot, we'll play in honor division next year.
The key element here is that we do NOT play against better players by artificially tying their hand behind their back. Likewise, we don't play against weaker players. They don't get to win with 50 points when we need 150, then go around saying they won (which they really didn't). If we want to play better players, we need to work our way up and then we'll have won the privilege to do so next year.
For local tournaments, for example my local poolhall holds weekly (or bi-weekly) 8-ball or 9-ball tournaments. They have 3 divisions with different prizes: division 1 players can win a flat wide-screen TV set, division 2 players a snooker cue, and division 3 players a bottle of scotch. When you come register, YOU choose in which division you want to play: if you want the television, you'd better be good. On the other hand, you may have a better chance of winning in division 2, but the prize is only a crappy cue. It's self-regulatory: good players will try for the better prizes, while lesser players (unless they're deluding themselves) will settle for a lesser prize and a bit of glory. But again, good players and lesser players don't mix, and lesser players don't get to win artificially.
With a handicap system, you pit Joe Blows against good players. The former think they're good because they can win, while the latter can lose even if they shoot lights out. Not to mention, if Joe Blow really sucks, the better player will be bored to death; I've seen that before.
When you separate players in several divisions, there's an element of pride being in a higher division. There's the haves and the have-nots, and the have-nots have work to do before they can even play against the haves.