Bard:
Pros
- can move while using every skill, has some managing issues since many off-GCD skills
- decent DPS for what they can do
- songs highly desirable for progression and easing most encounters
Cons
- lowest DPS class
- mostly used as song machine, silence player
- butt end of all jokes regarding ease

Dragoon:
Pros
- visually appealing class
- high DPS
Cons
- melee
- most popular class
- messing up your combo results in restarting combo entirely
- jumps are bad to use due to animation lock (changed in 2.1)

Hope this helps