Hi Practicar, Something that is "out of this world" is extraordinary and you were very impressed with it. As the words of the phrase imply, it is not something we would expect to experience in this world. Example: We managed to catch a glimpse of the aurora borealis and the view was breathtaking and out of this world. When we are "on top of the world", we feel ecstatic. We can imagine ourselves to be above all the worldly troubles in the world. Example: He felt on top of the world when she agreed to marry him. In your sentences: It was a lovely day and I was feeling on top of the world. (You were in high spirits and enjoying a lovely day.) Tracy showed us her holiday photos last night, the hotel she stayed in was out of this world. (You were so impressed to see that the hotel had excellent decor and paid so much attention to details. Probably, you have never come across a hotel like that.) Hope this helps. Cheers, Lance

Firstly, "on top of the world" indicates location, besides, it also can express a good mood or feeling. Secondly, "out of the world" means extraordinarily good.

On top of the world means you are delighted and super happy about something. Out of this world describes something that is amazing/unbelievable.