The subject of the first sentence is "day", so the question ask for a description of the day. What sort of description that asks for is open ended and depends on context. The subject of the second sentence is "it", so the question ask for a description of "it". What that refers to depends on context. You cannot say this sentence in a context where the speaker and listener have no common understanding what "it" refers to. Both sentences are 100% natural.

‘What was it like?’ tends to be an open-ended question giving the respondent latitude to talk about whatever was important to them. It could cover things like their feelings or psychological situation. ‘What was something like? is more specifically tied to the ‘something’ but still not confining. In the case of ‘something’ being ‘that day’, you might talk about the schedule or the weather but you could also talk about the effect of that day on you.

Both of these are good. We use both of them. (En Estados Unidos, quiero decir. Las personas de Inglaterra, Australia u otros países de habla inglesa pueden tener una opinión diferente.) Good luck!