[Arkorobotics]

Personally I would use electromagnetic actuators. But if it has to be between pneumatics and hydraulics I would choose hydraulics because:
a) really smooth
b) they can be accurate, and extend to a specific distance, rather than pneumatics which is more like point "a" to point "b". there is not a point "a in half". (example: you have a 6" stroke piston, but sometimes you want to extend 4" then like 5" then back to 3" (such as a car bouncing around in the game). A hydraulic can do that very accurately (depending on your equipment))

here is the cons:

a) really messy
b) leaking may happen so make sure you have a "gutterish system" (I really do not know how to prevent leaks, so you might want to search up on that)

Well good luck on the chair, it really sounds like a lot of fun.
Post pictures when you are done, I would really like to see it.

P.S. : http://www.bushleagueracing.com/how_it_works.htm
(this link might give you an idea.)

Motors also can work well (example: the van door motors that come in the KOP)

Good luck