Merit system is what I call a system where those who lead the guild make the decision who gets which drops. The result is often that the guild is stronger and thus everyone gets better drops faster than through the DKP system.
A simplified example from EQ (because I really don't know enough about end-game FFXI: In order to beat a certain mob, you need a warrior that has 10,000 hit points, and you need 3 clerics (whm in EQ) that are able to have a healing chain set up that they can sustain for 180 seconds.
Unless the guild has a warrior and three clerics who can do this, they can not kill a certain mob, no matter how hard they try, it's simply not possible.
In a DKP system, no one warrior is initially favored, everyone who participates equally has a more or less equal shot at whatever drop to improve their warrior. This results in a dozen mediocre equipped warriors, none of which has 10,000 hit points. It takes weeks to make the dozen warriors mediocre, and probably months to make one of them outstanding enough to break 10,000 hitpoints. The same with the three clerics.
In a merit system, the guild recognizes the need to have a warrior to break 10,000 hit points. The guilds goal is to kill this one boss mob, kill him over and over to get good loot. In order to kill the boss they need a 10,000 hit point warrior, and three awesome clerics. The guild does everything they can to gear those four people up as quickly as possible, and they spends weeks and months killing the boss the DKP guild can only dream about at that point.
DKP systems are getting more flawed the longer they run. Long standing members accumulate more points than they could ever spend, and feel entitled to bid on gear they don't need, just to spend points. etc etc. One could write a book on all the pitfalls of DKP systems, from attendance, to distribution, to point decay, to point caps, to spending caps, it's like a neverending spiral.
For many guilds (linkshells) a DKP system is the only workable solution, and as long as those who participate realize that no DKP system is perfect, it's all good.