Either boat should be OK on a low water Middle Fork, but you could carry more gear on the raft, and I think the raft would have less hang-ups. We take both rafts and cats on our September trips. Ideally you would fly in to Indian Creek. That's what we always do. I usually take my fly fishing gear, but only fish while in camp. Trying to do the "bump & grind" solo on my cat takes every bit of my attention. With 2 of you, one can row & one can fish. Whichever boat you take, run your tubes a little soft. It really helps you "slime over" the rocks instead of getting stuck.
Another suggestion, if your main focus is fly fishing, is the do the Southfork Snake below Palisades Reservoir. No whitewater, just swift moving water. Good scenery, good camp spots, great fishing. There are multiple places to put-in. We usually do the Conant to Byington stretch which is 25 miles, or you can put-in below Palisades Dam and run to Byington for a 39 mile trip. In the Conant to Byington section there are marked camps that you must use, and you need a groover & firepan. Stop at the Conant ranger station to fill out a self-issue, free camp permit, and get a $3/day parking pass. Southfork Outfitters (at Conant) does car shuttles. We often do a 4 night, 5 day trip. Very relaxing, with great fishing.
Have fun, whatever you do. We launch on the Middle Fork from Indian Creek on Sept. 12.