NFL Network is the best for rounds 1 and 2 because they have the most "polished" broadcast and viewing experience IMO. In those rounds, where the players being selected are generally well known and have been heavily scouted, NFL Network's analysis is as good as anywhere else in my experience.
When you get into the late rounds of the draft, if you still want analysis, you are better off switching to PFF etc. NFL Network guys aren't draft geeks. You can tell when they start to no longer know anything about the players left on the board, because they stop talking about the draft picks entirely, and just interview earlier draftees while a ticker runs across the screen to show you who is being selected.