+0
This is a ground breaking idea; it will change the world.
... an innovative idea ...

Hi,
Do both of the above mean about same t to you? Thanks.
+0
I prefer groundbreaking. It emphasizes how revolutionary it was. An innovative idea might save some money, come up with some new perspective, but it doesn't have nearly the same degree of "Wow!" as does a groundbreaking one.
Comments  
I'd use "innovative" because "groundbreaking" is something more natural with "discovery". An idea needs an implementation, or, at least, a more complete form (theory?) to "break the ground". Just my opinion... 
 BarbaraPA's reply was promoted to an answer.