How do I determine if I should use a pneumatic or hydraulic press machine?

The main difference between pneumatic and hydraulic press machines is in their power (or force, to be technical).  A hydraulic press can produce substantially more force than a pneumatic press, but the pneumatic variant makes up for this by being faster, cleaner, simpler, easier to work on and lower priced. In industrial manufacturing, pneumatic presses are preferred for component assembly and fabrication tasks where human safety is paramount, and hydraulic presses only where huge forces are required.