My internal frame camping backpack goes on camping trips, but...
...my go-to European travel bag is an internal frame backpack from Eagle Creek. After I pass on, there will be multi-step trials to see who earns the right to inherit it. I've used it for 16 years, and it's dedicated to overseas travel only.
It's rectangular in shape, so no problems there. While I do own a RS Convertible bag, it's a bit too saggy for me unless packed full (usually not a problem for me!), and I really miss the good padded hip belt and especially the sternum straps - those, with the good hip belt, make a huge difference in where and how your bag rides. It prevents it from swinging and from messing up your center of balance. Internal and external cinch straps are important (and I use packing cubes, FWIW). With that baby on and packed full, I can run after many a train without worry that I'll get thrown off-balance. Don't ask how I know this ;-) I can also not worry about getting off-balance while climbing up many flights of stairs. You and your bag are One when worn properly; you'll forget you're wearing it, no matter how much weight you're carrying. Seriously. I've never had a problem with taking it on the airplane (do you really think I'm checking My Baby?!? Over my dead carcass!), since the dimensions are the same as every other carry-on bag - and without wheels.
As for being a theft target, every other person is wearing some sort of backpack; I look waaaay more aware of my surroundings than many others do and that's what makes someone else the target. All of my zippers can be locked.
As for sweating, that's not hard for me to do in any case (sigh). Backpacks do make me more sweaty, and I HATE that, but to a lesser extent so does pulling - and often lifting - a roller bag. While someone might make a go at my rolling bag, they aren't gonna get that backpack off of me LOL! Plus, I really like the hands-free nature of backpacks, so I'll wear them as long as I possibly can. One's posture is better with a good backpack worn correctly than with a bag that must be pulled, so less chance of injury. My bag only weighs a few pounds, even with those sturdy metal buckles, and it weighs half of what my (lightweight) roller bags weigh.
I've toyed with using a roller bag for European travel to avoid the sweaty back, but I just can't ignore the convenience of my backpack...yet...but I have started using rolling bags for domestic air travel. Yep, RS Bags; how'd ya guess?
[If you'd like to be considered for the Last Will and Testament Trials to win my backpack upon my demise, please send me a PM; I'll be sure my Future Attorney has your info ;-) ]