I think 很小 is smaller than 小小.

Yes, it is almost the same, but FYI, 小小的房間 is like kid's talk or someone try to be "cute", because it is 疊字, like 大大的樹, 吃飯飯, 喝水水, 說說話,,, so I will suggest a growing up man don't speak that way, unless you are reading a story book to your children.

It's different wording the same meaning.

小小的 is a cute way to say something is very little.

Edi Wang and Chuck Tan are right. I don't think the two rooms have a different size. The speaker is just using a different tone. 很小的房间 is smaller than 小房间, but both are emotion-free ways of describing a room. 小小的房间 doesn't feel bigger or smaller than 很小的房间; it just feels "cute"; you would say that to a child, or to emphasize how tiny and cute a room is.