I main BQ and played ES for a while.
I can't say a lot about FL but from my experience BQ and ES usually deal more damage in PvE.
BQ:
+ One of the best bossing classes in the game
+ You don't have to put Crit into your sockets because you can use the force passive Indomitable Will (you can socket boss dmg instead)
+ Unique and rewarding playstyle
- Her clearing isn't great
- You have to buff yourself really often. (2x Brutal Cutter, Iron Body, Shade Illusion)
- If you play with Indomitable will and thus don't socket crit, your CP will be very low even though you deal a ton of damage.
- If you don't master i-frames you will die. A lot.
- No support abilities
ES:
+ Best Clearing out of all Elesis
+ Can increase the damage of allies with War Cry Mod and one of her passives
+ Low MP Consumption
* Her Bossing DMG is lower than BQ's but still good
tl;dr:
BQ: Bossing class
ES: Allrounder
FL: ???