My guild switched to DKP a few months back in reaction to constant whining about loot council decisions. I'd have attempted to make the decisions more open and understandable, but that has limits. So I might have just kicked the whiners instead.
Psychologically, DKP isn't the same as loot council. It has some benefits, some things which are the antonym of benefits. Costs! Losses?
Aw, nothing dropped :(
On the plus side, it gives you something to gain even when the boss doesn't die or nothing drops for you. Even better, if nothing drops that I want, it increases the chances that I'll win it in when it does drop.
On the downside, if I happen to be lucky with drops, there goes my DKP. This can end up feeling terrible especially when drops are uncontested. That was the case of most of my gear recently. I'd have preferred if uncontested drops were cheaper, except that encourages people making deals to cheat the system. So I did get a bunch of upgrades, but I now have no chance of getting any more. I know, it's kinda dumb, that I'd have gotten those upgrades over time anyway and burned the same DKP; so really all that happened was I got everything sooner rather than later.
BRB, cat's on fire
Loot councils can be more understanding of emergencies. They can accept that things happen and they don't mentally downrank you because something happened out of your control. DKP doesn't care, it only tracks if you're there or not. Leadership could grant points still, but once there's one exception, the floodgates are opened for all sorts of nonsense.
Social manipulation and guild benefit
On the other hand, loot councils can be influenced by sucking up or social manipulation. I'm not referring to the nice person getting loot over the jerk, since I'd have just kicked the jerk anyway. Instead I mean the person who is friends with the loot council, shows up regularly enough to not be obvious, but isn't there as much as other people, but due to social aspects ends up with priority. DKP is objective.
Or is it? A loot council can see that the somewhat equally geared people with a significant DPS gap, well who is it better to give the loot to? I'm not saying only the highest DPS (healing/tanking) should get loot, but it doesn't make much sense to throw away gear on bad players. Though if they're really bad, maybe they shouldn't be in the guild. DKP just rewards attendance. There can be more DKP for kills vs. learning vs. farming, but if the less skilled player is consistent, they're going to be getting the full DKP anyway. Perhaps that's still objective, but it's not practical.
See the Driven Draenei for a different take on individual accomplishment and DKP gain. It's about GDKP runs, but the idea translates well enough.
Choice and Understanding
DKP does have the big benefit of being choice. If you're low on DKP, it's because you chose to spend it. A council can be confusing. Why didn't I get that drop? I don't think I've gotten something recently, so what's going on? People hate confusion. To temper my earlier "kick the whiners" statement, I acknowledge that a lot of what is perceived as whining is really just confusion. Why did loot get handed out that way?
I prefer loot councils to DKP. They're just more human. But this depends a lot on trust in the council, both your own and that of your fellow guild members. My guild's council ended due to lack of trust from other members. I didn't like every decision, and frankly some were outright confusing, but overall I was happy with it.