Used by Blizzard, TERA.
In this solution, an individual item's appearance is changed to look like something else. The changed appearance is tied to the item. Advantages are that this makes a sort of sense within the fiction of the game world. As well, it is easy to tie different appearances to your different gear sets. You can have one look for dps gear, and one look for healing gear, and when you swap gear, your outfit automatically swaps.
The disadvantage is that because it is tied to your gear, every time you get a new item, you have to transmogrify it to get your look back. You also have to keep the old items around, and the process is a bit complicated compared to some of the other solutions. As well, each work set corresponds to one and only one cosmetic set. You can't switch between two different looks while wearing your healing gear, without re-transmogrifying everything.
Used by The Old Republic.
In this solution, the visual armor is a shell, and the stats come from mods which are inserted into the armor. Again, an advantage is that it make sense within the game world. It can tie into the crafting system, as there are now mods as well as armor to create. As well, it's fairly easy to upgrade pieces. Just rip out the mods from a new item and put them in the old item. A final advantage is that this doubles as a "reforging" system, because you can adjust stats simply by switching up the mods.
For disadvantages, again, it is a little complicated. Like transmog, each work set matches to one and only one cosmetic appearance. It's also pretty hard to compare gear in this system, as you have to compare each individual mod as well as the whole item. A last disadvantage is that set bonuses are a bit weird, because the set bonus is usually tied to the armor shell, and the mods are more generic.
3. Non-Visible Power Items
Used by The Secret World, Champions Online.
In this system, character power usually comes from non-visual items like trinkets or jewelry. The character's clothes are completely cosmetic. Advantage here is that it makes sense in the game world. As well, cosmetic outfits are completely decoupled from power outfits. What you are wearing has nothing to do with your power.
The disadvantage is that trinkets and jewelry are often unexciting. Very visual pieces like weapons and armor are often desired. They pack a 1-2 punch of good visuals combined with good stats. Also, an older piece of armor can carry memories, and reusing those older pieces can be a nod back to a previous time. For example, T2 Judgement is not just a great looking set, it's a reminder of the good times in Blackwing Lair. As well, while in the other systems you can choose to forego the cosmetic gear, and display your true set, in this system you can't. You have to pick a cosmetic outfit to wear.
4. Cosmetic Slots
Used by Rift, TERA, and LotRO.
In this solution, the character sheet simply has a second (or more) set of item slots. Items in the cosmetic slots are displayed, while items in the regular slots contribute stats. The big advantage is that this system is simple, easy to understand, and easy to use. The cosmetic set is decoupled from the work set. You can switch your cosmetic set without affecting your work set, and upgrade your work set without changing your look. Item comparison still functions correctly.
The major disadvantage is that this system makes no sense in the context of the world. Are you wearing two helms or two pants? It's a very gamist solution to the problem, and you just ignore the oddity of wearing multiple helms. The other options at least attempt to nod to the simulation.
Those are the cosmetic gear systems that I know about. In general, if you have to have cosmetic gear, I think straight cosmetic slots is the best solution. It's easy to understand and very simple to use in practice. Cosmetic armor slots parallel the regular armor slots. You can keep your power set while switching between multiple cosmetic sets. You can keep your cosmetic set while switching between multiple power sets.
The wearing of multiple helms is a bit weird, but it can be handwaved, and more or less ignored. Personally, it does not affect my suspension of disbelief. Your mileage may vary, however.