Spinning reels work great. I think if you are used to spinning reels, you’ll do fine with any of the aforementioned products. I highly recommend getting one with a bait feeder mode though for flathead fishin. Other than that feature, I’m sure all will perform. I have an Okuma Avenger in the ABF-50 size mounted on a white shakespeare cheapo rod, and it has pulled in sturgeon up to 57 inches and flatheads up to 43 lbs.
I personally prefer my baitcaster. The main reasons are a) I can’t hear my Okuma bait feeder on the spinning reel and Darren and John make fun of me a lot for that and b) I have better distance CONTROL with a baitcaster (though I think I can cast further with a spinning reel). When sitting upstream from a wood snag and casting back to it, I think I have better control by using my thumb to get my bait to stop before it ends up in the wood.
Now, I have to find some white rods to rig up my two new baitcasters reels that I got this fall.