So, I’ve run the near-gamut of 3/4 of the NA RP servers: WrA H, MG A, MG H, and spent a small amount of time on WrA A. While I have not roleplayed nearly at all on Emerald Dream, which is the only other large retail RP server that leaps to mind, I have friends who do and have done, so will attempt to give a brief summation of each option:
-WrA Horde was where I got my start, and honestly is pound-for-pound the best writing in an RP context that I personally have experienced. It’s pretty easy to find complex and engrossing characters, and it’s just as easy to develop interesting narratives and relationships with those characters on an IC level. However, a lot of the RP occurs in-game, and there’s not much by way of large “projects” in the vein of what you might hear about on Moon Guard. Most players tend to congregate in one part of Orgrimmar, and “events” do not often occur. However, it is by a wide margin the most populated place for Horde RP; walk-ups are always on the menu, if you would like them, and you will generally find more RP there than anywhere else for the Horde.
-MG Alliance is sort of the inverse of a lot of how I just described WrA H. A lot of the culture of that faction is rooted in large guild projects, though walk-ups are still entirely an option, and are usually dispersed throughout the entirety of Stormwind. You will find engrossing characters there as well, and can nurture plots and so forth with them, both in and out of the context of a guild or project. Unfortunately, the faction (and server broadly) is victim of itself pretty commonly, so OoC drama will sometimes flare up. Also, be forewarned; while the infamy of Goldshire has waned, the faction still contains all manner of tropes and cliches, both with respect to roleplayers and fantasy characters (for example, the Human Male Paladin archetype). It’s by far the largest roleplay community I’ve ever experienced, though Epsilon did take a toll on the population a little over two years ago; the server used to be competitive with MG in terms of overall population.
-MG Horde is, as many defensive individuals will rush to point out any time comparisons of the servers come up, also active. For the sake of the point, I will note that the largest Horde guild I can think of on the server is smaller than 150 people, whereas the largest guild on WrA is over 800. Walk-up roleplay is virtually nonexistent, so you will need to try and find a guild that works for you if you are set on Moon Guard for some reason. Horde RPers on the server do not lack in passion, but they are much more insular than their WrA counterparts, and no less prone to OoC drama in the way Moon Guard often is.
-WrA Alliance is a scene I know almost nothing about. I have found more walkup RP there than MG Horde, for example, but I don’t think I could name a single extant guild from that faction and server at present. I have heard that the roleplay is, as is seemingly true everywhere, available for people who want to look for it, but I wouldn’t even know where to begin such a search. The few interactions I’ve had on the server have been pretty pleasant, though.
-My friends on ED tell me that the server took a hit when Classic WoW was released and many people migrated to Grobbulus, but they also tell me that the server is, while much smaller than either MG or WrA, still active and facilitating things. Based on their accounts of the server, it seems the factions are much more balanced than either of the NA servers, which makes sense when one considers that the server’s focus is on RP-PvP. A few people don’t even RP outside of War Mode, so far as I know. If you are looking for a decent balance between content and roleplay, it’s a good choice because you can default to content if no roleplay is at hand, without feeling overly obliged by RP in the way that sometimes happens with larger servers.
Overall, any of these choices are serviceable, but Moon Guard is probably the best choice for Alliance roleplayers, and Wyrmrest is decidedly the best option for Horde roleplayers; Emerald Dream is worth exploring, as well. Even if it lacks fulsomeness like the NA servers, that doesn’t diminish the quality of the roleplay. There’s a reason you hear most people in the RP community endorsing MG A and WrA H.