What’s the difference? ほう vs もっと?

There is a similar expression with もっと:

犬が好きだけど、ネコはもっと好きです。　

Inu ga suki da kedo, neko wa motto suki desu.

I like dogs, but I like cats more.

The nuance here is that you like both of them but you like cats more.

Also, もっとcan’t be used to compare two things.

もっと食べたいです。 日本語がもっと上手になりたい。　　

Motto tabetai desu. Nihongo ga motto jōzu ni naritai desu.

I want to eat more (than that). I want to get even better at Japanese.

ほうが can’t be used for the above statements because they aren’t comparisons between two things.

X　→　日本語のほうが上手になりたい。 O　→　日本語のほうが英語より上手です。