I use the case that came with my reference alto, made by bam, I think. It's very durable and light in weight. A very important aspect of this case is the zippered pocket built into the lid. I carry music, bus and train schedules, a large comb, and I can even fit a small folding stand light into the pocket.
My back up altos both use Walt Johnson cases. The latches seem to be the best in the business, and the handle attaches to a metal molding. A very well built case, but heavy.
My tenor case is an skb with the little pocket on the outside. A good sturdy case. Latches could be better, but the price is right.
For baritone, I use a Berkley. I have shored up the inside with foam rubber, as protection inside of this case is very skimpy. But the shell seems to be strong, the latches are passable, and the whole shebang doesn't weigh much more than the horn itself. So I get hard case protection, with gig bag weight.
I try not to use the shoulder strap that comes with the cases. They seem to look strong, but the hardware that attaches the strap always wears thru, snaps, and unless you are fast with the hand, the case falls to the ground. I had an old time Selmer sax pac, those black zipper hard cases that came out years ago. The cover that you could buy for these had a sewn in strap with no metal or plastic hardware, but my sax pac has been retired for many years, needs the zipper replaced.
And the beat goes on.