Which is the best branch of engineering in coep ???

COMP - If you are looking from perspective of placement then this branch is the best among all.
There are plathora of IT companies come to COEP for campus placement. So you are ensured about the placement if you are a sincere student.
But the staff and faculty of this branch is not up to the mark. There will be hardly any lectures/practicals going around in this branch.
Also there are few professors who decides who will fail in practical exams, and might not be fair always. (But nothing serious.)

IT - Same as COMP. Just if you don't get COMP then get with IT.

ENTC - This is the "core" branch. "Core" being the word where most of the student fall for while taking admission.
If you are looking/thinking to do into ENTC field for career then go for this branch.
As per my experience, if you are NOT willing to do career in ENTC then SURELY don't go into this branch. Many people suggest that at least take core branch ENTC even if you are willing to do career in IT. (I also did same and wasted my 3 years in ENTC learning. [First year being common, didn't waste it.])
Though most IT companies allow ENTC students for campus placement, not all of them will. Also you are getting less priority while placements in IT as compared to COMP/IT students.

Instrumentation - Factuly/Placements are very good in this branch as well. But not sure about the details.

Metallurgy - 'Hat ke' branch. Not sure about the placements in this field. But not that great like comp.

Mechanical - There are good placements opportunities in this branch as well. So if you are interested in mechanical side then go for this.