The 500 is a base model whereas the 590 is a better built version of the same. The 590 has a thicker barrel, although that may mean little to nothing outside a military police environment, and the tolerances are a bit tighter. Think of it as the difference between the 870 Express vs the 870 Wingmaster. Not the best of analogy but it is a similar one. Another difference in the 590 compared to the 500 is the magazine tubes themselves. On the 500s, whether or not they are the 20 inch barrel Persuader or the 18.5 standard, neither can use a magazine extension, nor can the magazine spring be removed easily. This isn't a problem for many, but there are a few people it may be a problem for. The 590, in the 18.5 inch, version on the other hand can have an magazine extension put on it easily and for cleaning or upgrading the mag spring it is easily changeable as well. Yet another difference is that the 590 has a metal trigger guard and safety, the 500 doesn't.
The drawback to the 590 is that there are no barrels for them and it limits your options in that regard. At least with the 500 in the 18.5 inch 5 shot mag flavor you can get barrels with chokes or dedicated slug barrels. It really comes to what you are wanting the shotgun to do and how versatile you will need it to be. If I was going to only deal with the 5 shot version of the 590 it would become an 14 inch AOW SBS rather than a 6+1. If I just had to have a 20 inch it would be the 590 over the 500 Persuader, as you get a better shotgun with the same basic limitations other than the 590 is 8+1 and can mount an bayonet. For me it makes no matter anyway as I no longer own my old 835 or 500 Persuader anymore they have been replaced in the limited battery of arms that I keep. They were both very good shotguns and provided many years of useful service. It's up to you to weigh the differences and purchase what will fill your needs best. Good luck with your choice and I hope it serves you well.