Maybe, some performance comparison or some noticeable specific differences is what I want to know.
As I heard there is no really big difference. Hence, I've got one more question. For what purposes dozens of people spent their time to reinvent the wheel implement already implemented spec ones more?
The Sun RI 1.0 and the early versions of 1.1 were cluttered by nasty bugs. At that moment the MyFaces was the more stable alternative. Since 1.1.02 and 1.2.02 around early 2006 the new Sun JSF dev team did great work. Not only with bugfixing, but also with performance enhancements. As of now I dare to say that Mojarra is the better choice.
To get straight on your question:
For what purposes dozens of people spent their time to implement already implemented spec ones more?
Often to make it better. Or just because it can. Or for the imago. At least Apache is known to implement/enhance almost everything which is brought by (or missing in) Sun.
JSF was not, initially, open source. (eWeek in 2005: Sun Open-Sources JavaServer Faces) This prompted a couple of clean-room implementations to start so the spec could be used and distributed more freely. The terms of the Mojarra CDDL+GPL license aren't going to suit everybody, so there is still incentive to continue development under the Apache license.