Both are Browning-derived designs:
870...a manually operated Remington 11-48...which was a modified Remington 11 (JMB's Auto-5).
590...a modernized Remington 31...which was basically a side-ejecting Rem 17 (another JMB design...also used as the basis for the Ithaca 37).
The most durable shotgun in WWII? NOT the Win 12! The Remington 31 outclassed all others, according to Dean Grennell, referencing an Ordnance study.
So both bloodlines have great durability genes, but the feed latches in the Mossberg are clearly superior, at least to my eye. The carrier system is also more convenient. Breech bolting is equivalent, both using the Auto5 pioneered system. Dual extractors on the Mossberg can't hurt.
The thing with Mossbergs is that they are somewhat crudely made. The slightly greater cost of the Remington is made up for in better fit and finish, and the steel receiver.
You pays your money, you know the rest.