It can be a bit annoying to level on a PvE server if other players are trying to complete the same quest, but most of the time it is not bad. Leveling on a PvP server isn't all that bad as long as you avoid the obvious ganking hot spots or can level at odd hours (I can log in for about 30-45 minutes in the morning before I leave for work, and there is usually no one around). It depends on your server, of course. My hunter (who dinged 60 just this morning) was ganked about... 4 or 5 times, usually by level 70s running by who stopped to kill me then went on their way. Two 70s only killed my pet (no idea why) and left me alone. Yesterday a level 70 hunter left me alone in Silithus, as did the lowbie group he was helping.

The downside of a PvP server as a multiboxer is that you get more than the usual amount of attention, and if you happen to catch the eye of one of those MB haters who happens to have less of a life than they accuse us of having, they can spend a lot of time ganking you. On PvE servers it is usually your own faction that is the problem, constantly sending you tells and displaying their lack of intelligence. But I prefer to level via instances when I MB, so I haven't had any trouble. I do want to complete some Outland quests for my MB team before heading into the first instance there, PLing them with my shaman left them with mediocre gear.