There's no right or, wrong with this one, some are more vocal or, evangelical than others.
I do both, just keep in mind a few things.
1) Location. Does the destination you're going to demand or, would be much better if you utilized one method over, the other? If you're visiting known, well-worn destinations, then there's a very good possibility that rolling luggage will not be a hindrance. Lots of stairs, and trails...a backpack is nice to have.
2) Mobility & Awareness. Wearing a backpack-type to carry your gear, you need to be mindful when utilizing public transportation that you're not knocking people over and shoving them aside when you turn/rotate your body and your pack gets shoved into their face. If you don't carry a carry a backpack much, your situational awareness may not be tuned-on and you're likely to annoy/anger someone. The flip-side, with a roller, if you're apt to allow your bag to drag behind you where it appears you're pulling a train, there's a likelihood you're impeding or obstructing someone else's travel, thus you're causing problems, particularly if you abruptly stop in the middle of a thoroughfare or, walkway.
3) Comfort. You're the one responsible for your gear, traveling engenders a level of self-reliance, can you carry your own kit? If you have medical or physical concerns, then choose the method that'll work for you. It's ok to ask for help when lifting things but, you also don't want to be the one that is entirely reliant on others to get through the day as well. I took my parents (75+ yr old) on a 2wk trip and insisted they use 20" rollers; after visiting parts of Italy, they were entirely thankful that they heeded my advice and packed light. I had no issue with giving them an assist and their luggage was entirely manageable for them once on a sidewalk/walkway.