Can I use my Logitech Dual Action analog gamepad with the Freespace games? Also does the X-Box 360 controller work with them? I'm thinking of getting one soon.

search is your friend...
http://www.gog.com/en/forum/freespace_series/freespace_2_how_does_it_play_with_a_360_controller_nt

I would assume that you can. I tried with my old microsoft sidewinder gamepad and it sure works

Reading the thread I've linked to would have answered more or less everything you've asked, not only your question about the 360 controller. Let me quote a few things from that thread:

"A joystick and throttle is recommended for the game"

and

"Best gamepad I've played it with is a Logitech Cordless Rumblepad 2.
Mapped direction to left stick, y-axis on right stick is throttle, x-axis is rolls. etc. etc.
Not as good as a joystick, but still much more satisfying than a mouse."

The Logitech Rumblepad 2 is about the same as your Dual Action gamepad, so it should work for you as well. X-Box 360 controller does work with some tinkering, but I doubt it will be better for Freespace 2 than the Logitech gamepad you already own.

Thank you both. I'm planning to get a 360 controller but will be keeping my dual action as well so between those options it sounds like I should be just fine. :-)