I've never understood the appeal of one armed backpacks. Any I've ever tried are objectively worse than the two armed variety - smaller, move around more and don't stay properly fixed to your back, weird shaped for trying to carry things like books, not enough pockets . . . ugh.
If you need a small extra pocket, the fanny pack has been around since the '90s. If you need more storage, a regular backpack is better.
Yes, if your goal is to carry more, then a backpack makes most sense.
If you are just looking to carry keys/wallet/cell phone/glasses/etc, just essential stuff, a backpack is overkill and not as easy to access for wallet and phone.
But yeah, a fanny pack is just a differently oriented small bag, it serves the exact same purpose.