Hi, Ray—I think that only (b) is OK, though I shouldn't be surprised if I heard (a). Sentence (b) is elliptical for "We did a similar trip to your trip . . ." A trip can be similar to another trip. Trips and persons are not similar to each other.
Over the years, I've accumulated page after page of such errors, from both Oxford and Longman. It might be a good idea to let them know, but they seem to take a relaxed attitude to examples in their publications.
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