The EXP bonus applies to FATEs as well. I was leveling my..SCH I think at the time with a friend who had just started out. We were in the late 30s doing FATEs in Coerthas. We had just done the Eye event which rewards quite a bit of EXP and I asked how much he had gotten. Turns out it was quite a bit less than what I had received.
I'm not sure if it works for quests.
Your second question is very loaded and not easy to answer.
I feel that the community plays BRDs probably a little more. It seems very hard for people to get BLM to a level where it is not so boring (level 44) whereas BRDs don't really suffer from this. I would argue that BRDs are a lot more boring to play after playing both classes but that's just me.
Which is more sought after in what? BLMs and BRDs deal respectable damage. BRDs actually buff BLM damage which is why they are very complimentary in WP runs.
Which does the most damage in BiS gear? I would probably say BRD because BLM doesn't do well with movement mechanics. Right now, there are not many mechanics that require movement allowing BLMs near ideal situations where they can cast without being bothered. As soon as SE introduces fights with a lot of movement, BLM will suffer more. Then again, BRDs will receive a slight nerf next patch so perhaps that will even it out?
Right now, BRD and BLM are the top damage dealers and are probably the saftest classes to bring to a fight due to their long-range nature. However, you do not gain a melee LB from either class, DRGs buff BRD DPS, and MNKs have the ability to buff BLM DPS. Really, all DPS classes are quite nice at the moment. Some have to do a little more work than others but the end result is generally around the same given equally skilled players. Some may tell you DRGs lag behind but they should be receiving some buffs next patch that will fix their jump delays which will make it more enjoyable to play and easier to dodge things.
Ideally, for turn 5, I would like the following setup:
PLD (heavy mitigation at this point)
WAR (ability to DPS when they're not tanking; so much better than double PLD)
WHM (cure 2, benediction, shroud, medica 2, etc; they bring the heavy healing)
SCH (lustrate which ignores infirmity debuff, fairy buffs, shields and AoE shields, very efficient mana usage, they bring a pet to absorb fireball)
MNK or DRG (melee LB, buff other class damage, heavy controlled burst for conflags)
BRD (on demand burst for conflags due to amount of CDs they have to manage, songs for low MP, foe req. to buff BLM damage)
BLM (highest randomized burst damage over the course of the fight which isn't really ideal for conflags; AoE LB, lethargy for dreadknights, ability to virus and eye, highest sustained damage outside SMN)
SMN (another AoE LB3, battle res which is super important, a pet to possibly absorb fireball in an emergency, highest sustained damage that is not very subjective to movement, miasma for slowing dread knights)
As you can see, just about every class is there. Level what you enjoy and do well in your field.
Edited, Nov 30th 2013 3:34pm by HitomeOfBismarck