Generally speaking, I like hard shell cases.
I've had the polyfoam tenor cases (3 at one time) mostly because a) 2 of my ukes were shipped to me in them) and b) when I bought my first uke locally, none of the local shops had a tenor-sized HSC, so polyfoam was the only choice.
I've since given two of the polyfoam cases away - both to newbie players; one was carrying his brand new Kala in the cardboard box it came in, and one to the wife of a former co-worker who was getting him a ukulele as a birthday surprise (Thanks, Mim! He LOVES it!).
My two banjo ukes are in gig bags - the Firefly in a Bean Sprout Banjo Uke gig bag (and the closest I'll ever be to being able to own of of those gems!), and the Stella in my Cordoba's bag. oh, and the Outdoor Ukuele is in the Firefly's gig bag. Everything else is in a hard shell case.
Now the big However:
However, I recently got a used Reunion Blues Tenor gig bag from Gerald Ross, and I'm impresses with it. It is thicker by 2-3", and heaver than many of my tenor HSCs. But the convenience of the backpack straps is amazing, it is so well balanced I forgot I was wearing it one day, and the protection is undeniable. (And the price was way cool, too! Thanks, Gerald!)
Of course, Rick Tuner has stated for years that he keeps his personal ukes in Reunion Blues leather mandolin bags, and they are all that he needs. After seeing the bags, and the ukes in question, that makes perfect sense - especially with the relative humidity in San Jose, CA.
Here in upstate NY, humidity is much different, so I'll stick with the hard shell cases around the house, and consider the Reunion Blues bag as my #1 tenor bag for travel that doesn't involve an airline.
-Kurt