They are heavier. I don’t think hotter, but the waterproof fabric may have a bit of that. Of course that’s a big plus in rain/spills!
I have school age kids and I remember ditching the diaper bag before they were out of diapers because I hated the weight. Granted, I used shoulder/crossbody style because I prefer that to a backpack. That might make the excess weight more notable.
The plus is as you noted - there are more pockets and organization. If you want to bring a lot of stuff and are the type to maintain organization through the day then a diaper bag may be great for your needs. Personally I just throw my camera, phone, and wallet into a medium size purse and make do. But that’s a matter of travel style.