"Would you like to eat Chinese food or British food?"
想 means "think, contemplate, miss, desire, think about" and "want" but is also used to mean "would like." 喜欢 means "like" but cannot be used for "would like" as a direct translation of the English expression. We are getting into the realm of figurative and idiomatic speech. We can translate the English "what would you like？" to Chinese "你会喜欢什么？“ but in truth the Chinese just don't say it that way.