Learn English – Is there such phrase as “what more”

The difference is qualitative versus quantitative. When you refer to higher quality, you say better and when you mean a bigger quantity, you say more.
In a casual use, when detail really doesn't matter, and you only mean one over another in a general sense, you may use either word in most contexts.

In the given context, prefer takes over instead:
"Many users prefer the look and feel of A over B."

Here is a SWAG on this one. I suspect that it is actually an idiom based on analogy with the much more grammatical "sooner or later." I think that it is a transformation from "I'll get around to it" to "please do it now", and it is done in a parallel way. The parallelism requires the substitution of "or" with just one word "than" to keep the rhythm the same.

"Sooner than later" is a pretty new expression, picking up in the 1940s, though "sooner or later" is a much older and more common expression.

As to its grammatical correctness; it is certainly idiomatic and idioms seem to be allowed a lot of latitude on the grammatical front. Which is to say, "eat your heart out" Strunk and White.