I don't see how having a 3/4" panel makes it any easier to mount arcade parts. Most parts are made to be adjustable for different CP thicknesses, and if anything, thinner is usually better since you often have to end up routering out material to make things fit.
I don't think there's anything wrong with using different thicknesses for the cab and the panel. Most likely, you aren't really going to notice the edge of the CP, and if you brace the corners and edges at all, 5/8 inch should be fine. It's certainly a lot easier to work with 5/8" for making panels, since a lot of controls have very tight clearances--less routering to do, etc. I have several older components that were made for metal CPs, and I have to router and countersink like crazy to accomodate them, even on 5/8"!
The sides of my cab are 3/4" and the panels are 5/8", and to the naked eye, they both look the same thickness. You'd have to get a ruler or remove the panel and rotate it parallel to the cab sides to notice any difference...