I am curious as to what are the most popular software for managing the entire software development cycle. Would it be mostly Open Source, Closed Source or a mixture of stuff.
Depends, if this data is for you ( progress checking and planning ) or for someone like your boss or customer ( where you need a lots of data to present and "orientate" it the person you are presenting it.
No matter you have "All powerful software" you first need to make very good system ( not to go to much into details, to be easily administered, and it must be able to change frequently )