I have had both and can accurately comment on the characteristics of both.
There are good welded boats, and there are junk welded boats. A junk welded boat is still stronger than a good riveted boat; but the difference between those two was outlined by CedarRiverScooter. Rivets are easier to fix unless you have a welder set up to do aluminum, TIG being a better quality weld than a Mig. And you shouldn't solder aluminum with one of those propane torch aluminum soldering kits (notice I did not say 'welding' kits).
The characteristics. Riveted boats are lighter. Why? Because they're made from thinner material-generally speaking. The thin material allows the boat to flex quite a bit which over time allows the rivets to loosen up, and bucking them will tighten them back up for a few more years. Just don't leave them loose-because the hole that the rivet goes through can become oblonged and then the rivet may not tighten back up like it needs to. Riveted boats are generally speaking cheaper boats in a lot of ways. Performance on the water, they're perfectly fine for open water and for angers who aren't concerned with speed, handling, and/or how tough it is.
A welded boat is generally of a thicker material. It has to be in order for it to be welded properly. That characteristic makes the boat more rigid as a whole. The extra rigidity makes your trip feel more confident if you will. The thicker material obviously is less susceptible to major denting should an operator hit a submerged stump, tree, rock, etc. Keep in mind that not all welded boats are create equal. There are cheap welded boats. A lot of them are smaller and don't have horsepower ratings; they'll have a commercial tag on them. Those are the mass-produced hulls. They use a marketing tactic that I call "mass marketing"....in other words, build more boats and keep the cost down as much as possible to make the money. And the mass production really shows if you sit down and pick the boat apart. All MIG welded, no TIG welds (TIG takes longer but is far superior), use of really tall transverse ribs, permanently installed floors (not screwed or riveted in, so you can't access the soaked floatation under it-if it even has any), cheap wood transoms with exposed wood in some cases, etc etc. You know they're cheap if you see them. A better quality boat will have a removable floor, multi-piece transverse or any type of longitudinal ribbing, no wood exposed on the transom, a real horsepower rating, etc. You know quality when you see it. But that quality comes at a price-and usually you get what you pay for.
I have seen the cheaper welded boats fold up when they hit a tree. And I've seen better quality boats hit trees in flooded timber at full speed (~35mph) and bounce off, with a ding maybe, but never major damage. This is considered "confidence in equipment" if you can rely on the boat in those types situations, you don't have to worry about it.
Resale. Riveted boats are generally cheaper from the get-go, and should you decide to give it to someone else, or sell it, you'll take more of a hit than if it were riveted, supply and demand. Riveted boats are everywhere and a dime a dozen, so you have to compete with that market. Welded boats aren't all over the place, they're tougher less common and generally less "beat up", thus retain more of their value. I've been offered more than what I paid for mine when I bought it new in 2012, yes it's welded (.100ga 1548). It gets a l of comments, but it's nothing special really.
Welded boats can be formed and built differently, and the hull is usually stiffer, so they're generally a faster hull-even though they're usually heavier than a riveted boat. Less drag. Some hull designs just can't be reliably made with riveted panels.
Now those who haven't had and used both designs can't accurately say that one's better than the other, but I have owned, operated, and enjoyed both styles. If I were buying another today, I'd buy a welded boat unless it was something I just wanted to throw into the back of the pickup and float around in a small body of water, say a pond, where it would have to be dragged or carried to the water's edge, or if I didn't care how badly I beat it up on the way, and then I'd get a riveted boat.