I actually think that dumbledore wasn't entirely wrong to compare the snape-james dynamic to draco-harry. it's just that draco is the james of it all, not harry. he's the one with the privilege, the loving parents who buy him nice things and send him sweets (which i'm also sure the potters did for james) and the more aggressive of the two.

perhaps draco wasn't quite as extreme as james in the end but things like the potter stinks badges, making fun of him publicly for fainting etc, all the rita skeeter stuff in GoF, trying to (presumably) get him to fall off his broomstick by dressing as a dementor, that is bullying. the nastier stuff draco did to harry and co. throughout the books was almost entirely unprovoked and unmatched by harry's actions towards him; draco fired the first shots trying to get harry expelled with the 'wizard's duel' when like, what had harry ever done to him other than not like him/reject his friendship.

I do think it's a less extreme version of snape-james as I said, but the parallels are definitely there, especially when you consider that it culminates in harry using sectumsempra on draco- a spell it's implied that sev created to use on james. it's somewhat more equal perhaps because harry is generally more popular than sev was at school, but there are also various points where harry is very unpopular, such as the entirety of OotP when Draco lords his status as prefect and then inquisitorial squad member over harry to torment him. like it is a rivalry but also draco is considerably nastier to harry and more aggressive than harry ever is to him.

harry typically holds his own better than sev appears to in SWM, but with the exception of HBP he usually has much more pressing matters distracting him to devote much energy towards hating draco. I also think Sev often could hold his own and probably did, that doesn't make it not bullying.