better / worse than より、のほうが

This is a little confusing if you think too much on this! But I suggest memorizing one or two examples and then you should be able to keep it straight.

わたし　は　いぬ　より、　ねこ　の　ほう　が　好き。
watashi wa inu yori, neko no hou ga suki.
I like dogs less than cats. (I like cats more than dogs.)

You should spend some time studying the above example to understand how the ordering works.

Notice in English we use either "less than" or "more than" and the meaning is understood by the order of "dogs" and "cats" BUT in Japanese this is also ok:

わたし　は　ねこ　の　ほう　が　、いぬ　より 好き。
watashi wa neko no hou ga inu, yori suki.