I'll admit to being a cat partisan, and we have four Jack's cats: 2 Pack Cats, a Cutthroat, and a stretch Flyer Cat, both with custom frames.
Having rowed and ridden rafts on some of the classic western US trips, I do have a basis for comparing the two, so here are a few thoughts.
Rafts have more wetted area, i.e.
are more fully coupled to the water surface. This means they require more effort to ferry or maneuver against the current. In big water with waves breaking into the boat, they tend to "submarine," that is fill with water and become massively stable while being impossible to maneuver. Self-bailers take a few minutes to empty out and in continuous big water tend to act like bucket boats.
Among the effects of this larger wetted area and water retention is that rafts tend to get stuck more often in holes and also to flip in reversing flows. They are also prone to "wrap" on rocks and jams when the current plasters them against an obstruction. A cat might high-center on a rock or get stuck against a jam, but it won't be pinned there by the current force (unless it has a full-width solid flooró mine have open grids that drain instantly).
Nice things about rafts are that on vicious cold windy days the passengers can huddle down low on the floor and stay warmer. They're much easier to load and can carry more weight. When you hit a wave, the water doesn't come shooting up through the floor and soak everything. They're probably better for small children: more secure, big rubber playpens.
I like the way a cat will punch through a wave and rise to the crest. I like being able to bounce through a hole rather than getting bogged. I like being able to pee through the floor, and rinse the muck off my feet without hanging off the side. I like being able to see the water under the boat and dip a hand in it. I feel closer to the river in a cat.
Practica: A cat breaks down into smaller components that weigh less. A cat with a breakdown frame will fit into a small car or a bush plane: better gas mileage, no trailer needed, but obviously more time to rig. It can also be carried out of a canyon or across a bushy floodplain in reasonably sized loads. A 16' raft, rolled up, is a heavy, bulky item, and a welded frame, likewise.
Being a tinkerer, I like being able to rework my homebuilt cat frames to suit a particular trip. I can change the width, the arrangement (rower forward or back), the number of bays, the passenger seating, and pretty much anything except the length of the tubes and the waterline.
Here's a 12 ft. cat with ultralight frame:
I built a separate gearframe that can mount front or rear. A deckboard adds seating for a passenger.
Our 15 ft. cat has a similar, double-rail frame and can carry two adults (and a big fat dog) for a comfortable 7-8 day trip.