Pretty much just "looks."
All other things being equal (prep work, etc.) a firearm specific finish is going to look better and more professional and usually be more durable for longer and under more use than a simple spray paint finish. Though you can make spray paint more or less durable through prep work and/or coatings, etc., it's pretty much never going to be more durable that Cerakote (e.g.)
Some people are simply more concerned with the paint serving a specific "role" (camouflage, breaking up the outline of the weapon, etc.) than looking good, while others want to keep their guns looking good for as long as possible.
This is not a judgment call on either perspective, it just is what it is. Some people want to refinish for a practical reason, some people want to refinish for aesthetic reasons, and some people want varying degrees of both/in between.
One of the more odd trends, IMHO - is the faux "distressed" finishes... especially when using Cerakote... I'm not sure I "get" using an expensive, durable finish to get the same look as you could have using Krylon with no prep... but people want different things. It is what it is.
~Augee