Is it wise to use the live action Justice League as a base for this debate; Superman was practically godlike in that film, and other heroes should've been able to hold their own a little more.
One of the problems with adapting a comic book character to the big screen when there's so many comic books of that character to draw from, is that their power and abilities is going to fluctuate so much dependant on what the director is trying to do with said character.
Unlike Superman, Aquaman has access to magical weapons should he choose to utilise them. It's no secret that Superman doesn't exactly have a defence against magical weaponry, so in that sense, someone like Shazam could (hypothetically) give Superman a run for his money.
Superman is great if you just want a durable brute who can take a punch, but there are other DC heroes out there that can offer more than that. When Hulk (also a brute) took on Thanos, Thanos had the Power Stone; there was supposed to have been a second fight in Endgame IIRC that had Hulk and Thanos (without any stones) battle it out, and it would've been a much fairer fight, but it was apparently cut, or not filmed or whatever.