1-They have great senses of humor
2-They have a great sense of humor
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In the UK we generally avoid "They have great senses of humour." In conversation we will go all round the houses to avoid it. We might say, "She has a great sense of humour. They both have". Or we'll simply say, "They have a great sense of humour."
When you Google "have great senses of humor", the examples found are mostly from social media rather than literary sources. Switch to Google Books and the result is similar. (In the UK, with 'humour', the first few books include 'Your Best Friend – Is You' and 'Catvinkle'.)
"They" can be used collectively, e.g. "The editors of The Onion have a great sense of humor," becomes "They have a great sense of humor." Or you could talk about two friends with very different senses of humor, e.g. on is droll and the other slapstick, so you might write, "They have great, though antithetical, senses of humor."
It's like "fish" or "fishes".
He caught two salmon and ate both fish.
Salmon and trout are related fishes.