On the one hand you could argue that it's a lot harder to balance three factions (or at least stop them from thinking they're unbalanced, as Mythic found out), but on the other it's probably more balanced than two factions in terms of population dynamics.
Exactly. While DAOC never could achieve "perfect balance" between the 3 factions, each faction was unique in its own way, while maintaining all of the primary powers of the others. NF really cemented this by standardizing all but RR5 realm abilities across the realms. However, it added replayability by giving people the curiosity to try out the other realm's way of doing things (I tried Sorc, Bard and Healer for CC, and decided I liked Healer the most, for instance).
The other dimension it adds is that when a fight occurs in a contested area, you have the potential for a 3rd faction to show up and mix it up, rather than just reinforcements from one side or another. I can't count the number of times that a battle was being won/lost when the 3rd faction would butt in, and the fight would get a lot more interesting.
A key here is to not cave to demands for everything to be perfectly even, and keep uniqueness between the factions, and to have more than 2 factions to provide unpredictability in PvP situations. Another good key from DAOC was the lack of instanced PvP. Sure, BGs could segment you by level-range, but it didn't limit number of players per side, nor were the main PvP areas limited. The other factor is population size. I don't think DAOC PvP/RvR happens the same if the population is much larger than what they allowed. Too many people running around makes for problems as well.