I'd say both are forms of jobbing. Doomsday at the time was simply too unimpressive an opponent to really sell as a credible threat. He had extremely limited powerset, no charisma, no real intelligence or skill. The JLA was trotted out to at least make the situation seem dire or important but that shows another weakness of modern writing where in the writers never really built up the skills to sell villains and threats as credible to the reader. The JLA's job was to make an unimpressive opponent seem impressive.
Superman's losses to Batman are frankly idiotic. One guy spends his average day fighting things considered beyond Mega-Events for the other guy. It's a Grizzly Bear fighting an infant and the outcome is obvious but Batman is more popular thus he has to win because that's how things work in the DCU. At least Marvel tries to keep some kind of semblance of a power structure so when something bizarre like Black Panther catching Silver Surfer in an arm hold happens everyone rips the writer for it.
The stupidest thing to me is that we just went through Doomsday clock which tried to explain why "THE DCU IS SO DARK AND STUFF" when the answer is staring them right in the face with this Batman/Superman rivalry that has been brewing since the late 80's. If you tell people that are looking for a power fantasy that all the power lies in being some angry dark hero then that's what they'll all seek to emulate. DC spent most of post crisis doing just that and Doomsday Clock should have been an examination of that. Why are the Batwriters drawn to picking a fight with a guy that has nothing to do with the character, why did the Superman writers spend years going along with it instead of putting a stop to it immediately, and is it really such a good idea to try and define your first hero by the behavior of a guy that came after him? Instead we got "something, something. Alan Moore".