One quirk I’ve seen with LWJGL 2 is that, on Xbox controllers at least, the triggers map to the same axis, with one trigger pushing negative values and one pushing positive. This means that if both triggers are pressed, this will result in the axis being 0. Also, on Linux, I’ve seen some gamepads get shown twice on the computer. However, this can pretty easily be fixed by telling your project to rely in JInput 2.0.9 as I describe here.
With LWJGL 3, on the other hand, my gamepad has a couple of the axis that share the same name as the bumpers. This breaks the remapper and prevents it from getting all the buttons working. This is rare, and I’m actively working on a fix for this, but
Besides that, I’ve noticed that the default remapper file in jme3-core tends to be configured for LWJGL 2. However, besides the issue above, I’ve found LWJGL 3 to be more reliable.