If both are correct, are there any differences between them?

  • 犬や猫が好き is another option. – dainichi Jul 8 '15 at 1:30

Both are 100% grammatical and natural-sounding, but since the two phrases are used in different situations/contexts, they are not interchangeable.

「犬{いぬ}と猫{ねこ}が好{す}き」 is said when "dogs and cats" have not specifically been mentioned between the speaker and listener.

The best example of that situation would be when someone asks you the question: 「どんな動物{どうぶつ}が好{す}きですか。」 = "What (kinds of) animals do you like?". If you like dogs and cats, you will say 「犬と猫が好きです。」. You can never answer that question by saying 「犬も猫も好きです。」.

Moving on...

「犬も猫も好き」 is said when "dogs and cats" have specifically been mentioned and they are now the topic of the conversation.

The best example of this situation is when someone asks you the question: 「犬と猫では、どちらが好きですか。」 = "Which do you like better, dogs or cats?". If you like both almost equally, you can say 「犬も猫も好きです。」. You would sound incredibly weird if you answered that question by saying 「犬と猫が好きです。」.

| improve this answer | |

"犬と猫が好き" = "I like dogs and cats (among animals.)" A typical answer to the question "what kind of animals do you like?"

"犬も猫も好き" = "I like both dogs and cats." A possible answer to the question "which do you like better, dogs or cats?"

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