It depends on if you are referring to a colour that goes by the name tree or not.
You could be in a paint store and looking at various swatches. You stop at one and say:
Oh! I like that tree colour!
In this particular case, tree would not describe a plant but a colour. (In the same way, you could say, "Oh, I like that red colour.")
If using tree in this specific sense, then your two sentences would not mean the same thing.
In a more normal context, however, all of these would be taken to mean the same thing:
The tree colour is absolutely beautiful.
The colour of the tree is absolutely beautiful.
The tree's colour is absolutely beautiful.
Having said, I would say that tree colour would be the least common way of phrasing it, and colour of the tree the most common.