I think more than anything, Eddie is just not funny in 3 nor is he trying to be. What was refreshing about this new one was you can see him actually trying and nailing most of his jokes.
I think John Landis said he never improvised for 3 and just stuck to the script. Eddie, at the time, didn’t want to be a wiseass anymore.
Apparently, the reason Eddie comes off as slumming it in 3 was that, per his later admission, he was in a bout of depression due to a string of massive flops he had at the time and just wasn't trying. It's part of the reason he disowned 3 and why he was so hell-bent on trying to get this movie made for 30 years. And if Eddie friggin' Murphy is slumming it, you know something's wrong. At least in his other bad movies like Norbit, Meet Dave, A Thousand Words, and Pluto Nash he's doing his best to be funny despite the material.
Looking at what he put out prior to BHC3, you can see why he was depressed. In the late 80s/early 90s post Coming To America, the guy was genuinely trying different things in his career and nothing was working. He did a fantasy-action/comedy (The Golden Child); did not work at the time, but has gotten a cult following since. He tried doing a political comedy (The Distinguished Gentleman); did not work. He stared in a horror comedy for Wes Craven (Vampire in Brooklyn); did not work. He did a sequel to his first big screen hit (Another 48 Hours); did not work. He tried being a romantic lead for a change (Boomerang); did not work. He even tried DIRECTING his own comedy (Harlem Nights); not only did it not work but it got overshadowed by a bunch of random shootings that forced AMC Theaters to yank the movie entirely, even if the shootings had nothing to do with the movie itself. So yeah, by the time BHC3 happened, he probably felt his career was dying and was not happy about that, so I can't blame him for that kind of mood. It wasn't until The Nutty Professor afterward that he really got his swing back and has been more consistent again acting-wise, regardless of the quality of whatever he's in.
And to be honest, I was worried he was getting to be in another slump again recently. Dolomite Is My Name was such a comeback for him that it felt like he was reinvigorated after his hiatus. But then Coming 2 America came out where he's barely the focus and the movie is just ok and then that crummy movie he did with Jonah Hill (haven't seen Candy Cane Lane, so can't judge there) and it just felt like Dolomite might have been a fluke. But then we got this and I'm happy to have been proven wrong.
EDIT: Updated to include The Distinguished Gentleman, as that caused further problems for BHC3.
