Appropriate leves give the same exp as a FATE completion. Many leves can be done, solo, less than 60 seconds start to finish. It's impossible to sustain the same pace with FATE grinding. If you're doing it right, they are hands down the fastest way to level, at least untill 44. Of course, leves are finite, and once you're out, you have to find something else to do.
After leves are expended, it's FATEs or dungeons. If your queue time is fast/instant, dungeons are probably the way to go. If you're sitting around waiting on a 20 minute queue, dungeons are about the worst thing you can do. Depending on how popular each new class is will make a BIG difference who can grind dungeons.
People anticipate DRK will be wildly popular, and will crash the low level tank queue times. People speculate DRK is going to draw a lot of players who just want to play DRK, and don't want to tank, or don't know how to tank, or can't tank, they either wont queue for dungeons at all, or wont hack it tanking dungeons, and will stop, we'll have to wait and see. I think it's true if you're leveling MAC, you'll probably instant queue every time the first few weeks, and if you're somehow leveling a melee between 30-50 you'll probably get /tells asking you to queue up. Weather or not it's worth putting up with players on brand new classes is a matter of opinion.
Anyway, in MY experience, FATE grinding from 35+ takes about an hour a level if you're with a party. It's arguably extremely boring, but I disagree that it will make you bad at your job. If you are familiar with the game, and can read tooltips, you'll be fine when you reach the level cap. If you're bad, it's not because you didn't level in dungeons, you're bad because you're bad. :)
I've never found dungeons (outside of roulette bonus, and DD spam) to be significantly faster than that. It might keep you from going crazy, but for me that's about it. FATE parties will be fast and plentiful, and people will be working hard. I fully expect the average fate party of 4 DRK, 1 MAC, and 3 AST will be the fastest route.