The mag tubes and barrels are different. The 590 has a threaded cap that fits over the outside of the mag tube. The 500 has a screw-like cap that fits into a threaded hole at the end of the mag tube. The 590 in the same barrel length will hold more cartridges.
The 590 A1 is the heavy barreled "military" model and will not accept a mossberg heat shield to my knowledge, at least without modification to the shield. The A1 also has a metal safety and trigger housing. The longer model has a bayonet lug.
As far as I know, the only difference between the modern 500 and the NON-A1 590 is the magazine tube and the associated differences in the barrel lug/ring. For a while there were some differences in the length of the slide action tube but I can't remember if they standardized that or not.
Older 500s and clones had different cartridge interrupters than the modern style also. And there are at least 3 different types of bolts/bolt slides, but AFAIK the recent 500s and 590s all use the same type of bolt and bolt slide.
As to whether you should worry about it... I vote no. You'll have a hard time wearing out a 500 or a non-A1 590.