Here are my thoughts:
Adhesive backed:
Professional looking
Permanently stays in place
can be applied to curved control panels
Plexi optional
Stays straight through use.
Adds protection to control panel surface
Can be a pain to remove after years of use and replacement art is desired.
Line it up wrong while applying and you could have a hard time fixing it.
Non Adhesive backed:
Can be removed at any time and reapplied (Important if your joysticks are mounted through the top.)
Plexi required, and plexi must be mounted well.
Needs to be sandwiched between plexi to stay flat
Can warp and shift with use, generally wont last as long.
Easy to replace
Moisture can get caught between art and CP
If you feel confident about your art, I would go with adhesive backed.