Not much difference
I've only handled a 500, and only once, but the main difference appeared to be in the magazine tube. The 590 series has the more conventional style, with a takedown screw that goes on like a cap on the end. The ring on the barrel goes around the tube, and the cap also holds the spring in.
On the 500, the mag tube has a permanently attached end cap that holds the spring in (you have to unscrew the whole tube from the receiver to get the spring out). The end cap has a smaller diameter threaded hole in it for the takedown screw. The ring on the barrel (isn't really a ring, even) butts up to the end of the tube, and the takedown screw goes into the permanent end cap. I think the screw is captive on the barrel.
The 590s are parkerized; 500s are blued.
590s have a parkerized bolt; 500 bolts are shiny.
As stated, the A1 version is where you get a real upgrade.