"Like something more" or "like something better"

I think that there is a very obvious answer to this question. The opposite of "better" is "worse." The opposite of "more" is "less." So, which of these sentences sounds correct:

I like dogs worse than cats

I like dogs less than cats?

The answer is clearly "I like dogs less than cats." The sentence "I like dogs worse than cats" would be flagged by any native speaker as being incorrect. No one would ever say that. The answer, in my honest opinion, lies in semantics, not grammar.

Think about it deeply; it simply doesn't make sense to say that you like something better. The word "better" tells you something about the worth of something. Whereas the word "Less" tells you something about a quantity (less butter) or about the perceived strength of something (less light). To increase or decrease the force of your 'liking," only two appropriate words are available to you: you like something more, or less. You can't like something better or worse, because these are words that comment on the value of liking, not its intensity.

To say "I like cats better than I like dogs" means, semantically, that your liking for dogs is somehow better than your liking for cats. And it's obvious that that is not what most people intend to say when they use "better" in this context.

What they mean is that their liking for dogs is GREATER than their liking for cats, not that their liking for dogs is in some odd way BETTER than their liking of cats. Dogs may be better than cats, but our liking of dogs can't be better than our liking of cats.

Of course someone might think that it is better to like dogs than it is to like cats. But there are no "better" ways of liking something.

More is, to me, the better of the two. Perhaps you could avoid all ambiguity and instead of:

I like Dogs more.
I like Cats better.

you can try:

I prefer Dogs.

You can use either, both are short versions of comparisons. I like cats better than dogs, but dogs more than pigs.

Historically, like well and like better were the norm. (You'll find it in Shakespeare.) British English has dropped this usage, and opted for the more consistent like more, but still retains like well in expressions like well-liked or best loved.

American English has retained like well.