In reverse order:
I have the 590-A1 and love it. As the only shotgun so far in this household, it has been used for target shooting, clay shooting, grouse, pheasant, and duck hunting, and 3-gun competitioning. It has done well in all situations. For clays or hunting you have to get a shot off quickly due to the spread making longer distances less practical. After patterning a bunch of ammo brands I have found some loads that hold tighter groups. The capacity is great for the 3-gun competitions. It shoots slugs much more accurately than I had anticipated it would.
I have attached a Knoxx SpecOps stock for the benefit of adjusting to the correct fit for myself, wife, or others. I also love the recoil reduction mechanisms and have enjoyed a day spent shooting 3-inch magnum slug and buckshot rounds. The barrel got pretty hot but the shoulder was fine. My wife also got some great looks when she took it out for clay shooting with some friends.
My original configuration was the normal synthetic stock, which I used for a while. I prefer the simpler stock which serves me well. I did replace the butt pad with a skinnier one to improve the fit. That half inch made more of a difference than I thought it would. I have read the same thing dfariswheel mentioned about the Speedfeed losing rounds due to recoil.
No side saddle info to help you there.
I have the metal trigger group with the 590-A1, no problems there. I have heard that CaCruisin, who works at Knoxx, has put the plastic trigger group of a Maverick (same company, cheaper brand) on his Mossberg because he likes the safety placement better. He's had no problems with the plastic group. Others may have, but I don't know of them.
The capacity of the 500 is 5+1 while the 590 can have up to 8+1. The 500 and 590 can have a heat shield for the barrel as a factory installed option. The 590-A1 does not accept that heat shield due to the heavier/thicker-walled barrel.
Which ever you decide on, practice, practice, practice.
-Research