One of the main problems with the Emperor boils down to one of the main problems with the Horus Heresy in general.
Inconsistent characterization.
Which makes sense, because of the nature of Black Library. There’s so many different authors writing so many different characters, shit is bound to get jumbled up.
In one of Mortarian’s books, I believe it’s called the Pale King, the interaction he has with Big E paints a very different picture to the one we got in Master of Mankind or the First Heretic. Same with when Perturabo talked with him.
In both of those instances, he comes across as far more human than in others. He comes across more as a father than, say, his interactions with Angron or Lorgar.
Fundamentally speaking, the Big E isn’t really what we’d call a character. He’s more like a plot device or set dressing for whatever given author is writing him at the time.
As a character/person, I like Karl better. He’s more consistent, whereas the Emperor can almost come across as schizophrenic from one book to another.
I don’t know if he’d be able to handle the WH40k universe any better than Emps, besides maybe not being as bad with some of the Primarchs.
Inserting the Emperor into fantasy is rather pointless, because he’d basically nuke the setting. Asking if he’d be a better ruler than Karl is rather pointless, when he just starts marching into chaos/skaven/vampire/ork strongholds and cleansing them in not holy fire.