There is a very subtle difference between the two statements, although they may sometimes be used interchangeably. In the first statement, you are speaking in the present tense (It's = it is) about what you thought of something in the past. To reword it for clarity: "It is, at this time, not how I thought it was, at a time in the past." It could have been how you thought it was in the past, but it is not currently that way. The second statement (also speaking in the present tense) is saying: "In the past I thought of how it would be at this time, but my thinking was not correct. It is not that way" The statement does not specify how you thought it was in the past, but how you thought it would be at this current time.

I think it depends on the meaning, the first is when you know about something that is already there then you find it you discover that it wasn't what you thought.. The second is about an experience or something that you thought to be easy but when you try it you find it hard or vice versa, mainly it is used describing a state or a situation.

"It's not how I thought it would be." = It has turned out differently to what I expected; The results turned out differently to what I expected . "It's not how I thought it was." = The thing is totally different to what I thought it was.