To start with, I'd like to explain the basic premise of what a loot system is -- not that I don't think people don't already know that, but some people have different views on what a loot system should even accomplish. I think it is best if I set down a solid foundation on which to base this article.
At the core, a loot system is merely a concept for distributing loot in such a way that it is equitable, balanced, rewarding and timely. An equitable loot system is one that has some function of equality within it -- essentially, trying to avoid the drama of a select group of friends' always getting the best loot first while the rest suffer without. Basically, everyone should have the same opportunity for getting gear as everyone else.
A balanced system is one that isn't subjective to abuse such as favoritism, price fixing, hoarding and so on.
Now, while loot distribution is all about rewards in and of themselves, some players like to have the loot system itself be rewarding. This means different things to different players. Some people believe that loot should be based upon merit, in the sense that players who contribute to the guild's success (via donations of materials, good attendance, high performance, etc.) should be more deserving of loot than others. Not all players believe this, and not all loot systems support it, but it is a factor to consider.
Finally, a loot system that is timely references the frequency at which a player gets loot. In some systems, players may be able to get a new item every week (provided it drops) or even multiple times per week; others may be structured so that players generally only get an upgrade every few weeks or possibly once a month.
Do all of these loot systems cover those aspects? That's for you to decide.
Dual Token System (DTS)
The Dual Token System (DTS) is a rather basic form of loot distribution that operates primarily on an open roll set-up. Within the DTS, each player within the guild is given two "tokens" at the start of every new raid lockout. For times when there are multiple raid instances per ilevel, such as what we had with Naxxramas, Eye of Eternity and Obsidian Sanctum, a guild may choose to tie each of those raids together or treat them as individual lockouts. The two tokens that are given to the players are a "need" and a "greed" token. When an item drops, it is first placed on roll for those who need the item; that is, they wish to spend their need token in a chance to get it. All the players who wish to use their need tokens either announce so in /raid or whisper the loot officers (depending on the guild), then make a standard /roll for the item. The highest roll gets the item, and the winner loses his need token; all those who rolled but did not win the item get to keep their tokens.
If, by chance, there is no one who wishes to need the item, it is then offered up for greed. At this point, players can choose to spend their greed tokens for a chance at the item; they make another /roll to win it. Again, the highest roll wins the item, and the winner loses his greed token while everyone else gets to keep theirs. If no one in the raid wishes to spend a need or greed token, the item is then placed up for an open roll to anyone within the raid -- at which point if no one still wants it, the item is sharded.
Should it ever occur that everyone within the raid has spent either all of their need or all of their greed tokens, the guild can then choose to give everyone in the raid another token to spend within that lockout. Within this system, tokens are not kept or carried over in any way; they reset each week, and players can never have more than one of each type of token at any given time.
Many of the complaints about this system center on the fact that there is relatively little pressure upon select specs to spend their tokens on certain drops that they might actually need. For example, if a guild has only one or two holy paladins, they may not feel compelled to spend their need tokens on a piece of plate healing gloves given that no one else could feasibly use; this allows them to save their token for items they would have to share with other specs, such as weapons, rings or necklaces. In some ways, the system is protected against this in that there is no preference given to main or off specs; therefore, a protection paladin could choose to use a greed or even need token in order to get a DPS or healing item. Although holy paladins are unique in this respect, other classes are generally not as safe from such situations -- which does work for the system. Paladins will often use mail items, druids will often use cloth items and so on and so forth, with multiple classes and specs often not remaining within their top-tier armor type; thus, it's feasibly possible for a player who believes a piece of loot to be safely theirs find it snaked out from under them.
It should be noted that there is no sense of reward within this system, as it is falls high up on the scale for being equitable; everyone gets the same number of tokens and rolls are completely random, so there is no regard given to merit, skill or other outside factors.
Floor Log Rap (FLR)
Floor Log Rap (FLR) can exist as either a DKP variant or as reputation variant, depending upon which the guild chooses. Essentially, the FLR awards players either Raid Attendance Points (RAP) or Guild Reputation Points (GRP) for various things including showing up on time for raids, downing a particular boss, working on progression, or other activities that contribute to guild success such as farming consumable mats. Each player is then placed within a loot tier level based upon his current RAP or GRP totals, in a formula similar to this:
Loot is then distributed based upon the loot tier that player is in at that given time. Players in higher loot tiers have preference over players in lower tiers. If multiple players within any given tier seek the same item, then a random roll is performed and the winner of that roll is awarded the item. After receiving an item, a player's RAP/GRP is then reduced by an amount determined within the system. Multiple methods are possible; the player can lose a percentage of his current RAP/GRP, he may lose a flat amount determined by the item type (tier pieces or select items may be worth more RAP/GRP, while items from older raid instances may be worth less RAP/GRP), or he may use a log-based formula reduction (which can become slightly complex and is usually avoided).
The major benefit of this system is the exponential growth between loot tiers, which allows players to progress between the lower tiers faster than a player who seeks to hoard his RAP/GRP can advance into the upper levels. The rate of this advancement can be further influenced by the way points are docked or earned by players, allowing for a high amount of flexibility in how players are rewarded. Hoarding is also deterred by the use of open rolls within each tier, so unless a player is able to reach a higher tier (which is always going to take longer than it would for a player to catch back up in rank), he won't have a higher chance of getting an item than anyone else.
Further, due to the rapid nature of the system, classes that pick up multiple items for various specs that they might perform generally aren't overly penalized within the system, as they can usually catch back up rather quickly. This also helps to prevent items that are usually considered minor upgrades by players from being sharded, as there's little incentive to hold onto points.