another joystick issue/question

Here's the story: purchased Flashback 2 system on ebay, one joystick totally did nothing. Purchased 2nd Flashback 2 system, everything worked. Was in a hurry & didn't label 1st non-functioning joystick, so tested each one with the 2nd console I purchased. Hmm.. both worked!  So.. re-hooked up console 1... retested.. same thing.. one of the original joysticks doesn't work. However, both joysticks from console 2 work in console 1.

So.. is it just a freaky combination of the console plug & the joystick plug?

Should I just run with the combinations that work? (giving one each to my 30 something sons)