I wouldn't recommend a rolling backpack. If you carry it as a backpack, the wheels add too much weight. Many European airlines restrict the weight of your bag as much as the size.
Also, Rick's (as well as Campmoor and others) convertible carry-ons are a lot like carrying a sack of potatoes - whether they come with a waist strap or not. They don't have much structure or internal support to make them a true backpack. I compensate by rolling my clothes and packing in a way to add some level of structure to my bag.
Right now, I'm using a Campmoor convertible carry on because it's the cheapest, lightest, as well as similar in all other respects to more expensive bags. I really like the luggage style zippers. Anything resembling a ruck sack is going to be a pain to get in and out of. Most backpacks are made too long for carry-on requirements so have to be checked, which is another reason I don't use them.
Although convertibles really aren't great "packs", I find I rarely walk over a mile (usually a quarter of that) so I value the packing convenience and light weight more than I miss something easier to carry.
My wife uses a 20" roll on and is happy with it. She only carries it when she's going up or down stairs or hopping on or off buses and trains. She has a Hayes USA X-case - again purchased because it was the lightest weight we could find. 20" ensures it always fits - a 21" inch, with rigid wheels and handle, might exceed the carry-on limit.
We have multiple trips of one month and one of six-weeks using only one carry-on each (no additional "personal" item). While my wife gets tired of the clothes she packs, neither of us miss checking bags or being weighed down with extra stuff during our trip. We wash socks and underwear almost nightly in our room and stop at least every other week for a full wash at a laudromat.