I'd say it depends on who is doing the majority of the care for the horse, and in the case of a sale, who you are dealing with the most.
In general, I'd say a bad trainer is going to do more damage than a bad owner, but that answer sure doesn't cover a small two-bit trainer that has one or two horses versus an active owner with a ton of horses.
If we're talking what's more dangerous, a bad owner or a bad trainer, I would say the bad owner is worse, and here's why: a trainer with a bad reputation usually got that reputation from being abusive. Hear me out. These trainers go to great lengths to hide the abuse. Often you will have a horse at a healthy weight, with a healthy coat, great nutrition, feet are well maintained, etc but they will be be abused under training. A bad owner could result in a horse starving to death or living in darkness, away from the public eye.
In terms of reputation alone, a bad trainer is worse. Trainers get away with a lot of crap. If they've screwed up enough to have a reputation for their crap, that means they really, really are doing something wrong. An owner with a bad reputation may be willing to learn but made honest mistakes along the way. In my experience it's a lot easier for owners to get bad reputations than trainers, mostly because nobody is threatened with lawsuits for speaking their mind about an owner.
I've seen owners get bad reputations over honest mistakes while trainers got away with murder because people were so afraid of being sued they never spoke their mind.
I'd say that in general, a bad trainer is worse, because they can teach those bad horse care/training things to many others that don't know any better, or do things to good owner's horses when they aren't around to see it. They can also get the owners of horses hurt, whereas a bad owner usually doesn't have as many horses under their care to injure or have hurt someone else.