I choose the 1300 over the 870 because the action is smoother and more reliable. The 870 is more popular because Remington won several contracts with large police agencies. Remember, local cops are equipped by bureaucrats who wait for the F.B.I. to select a piece of equipment, then decide that this is exactly what their department needs. Remember, the F.B.I. decided the 10mm was just the ticket, then agents started having problems qualifying, then agents started having problems with over-penetration causing the F.B.I. 10mm-Lite, yada-yada-yada...
My point is that just because "the police" use a particular weapon, that doesn't mean it's the best. Doesn't mean it's not either, just don't believe everything you read in a gun magazine.
Sorry for the rant, just tired I guess. I think either shotgun will serve you well, the 870 will just require more money to get the same results in the long run. JMO. YMMV.
May your lead always hit center mass and your brass always land in your range bag.