Let's break it down.
First, let's make a list of all the centers who should be considered. For this exercise, I will make completely arbitrary decisions as to who is and is not considered a center (for example, LaMarcus Aldridge is not considered a center).
It is my opinion that, this season, Joakim Noah is the elite member of this group.
To look at overall statistical contribution (that which can be calculated in a box score), I feel PER is a solid basis for judgment. Based on this alone (and Estimated Wins Added, which is simply PER multiplied by total minutes played), Joakim is clearly having a fantastic year statistically, with a PER of 19.27, and an EWA of 7.2 (meaning Joakim is worth 7.2 wins more to the Bulls season total than a replacement NBA center, such as a Nazr Mohammed).
DeMarcus Cousins is in the lead in the pure statistical category. By quite a bit. Boogie has a 26.11 PER and an 11.3 EWA. Boogie puts up numbers. But, Boogie bad at defense. Boogie horrible teammate. No way Boogie better than Joakim. He probably will be eventually, but not now.
Marc Gasol has been hurt too much. That is all.
Dwight Howard is an interesting case. He used to be the best. Now, no one likes him and he's not nearly as good as he used to be. He is slightly superior to Joakim in terms of statistics. But Dwight's defense has fallen a long way from his incredible Orlando days. Dwight also seems to lack in certain leadership areas. Also, he's annoying.
Andre Drummond could easily top this list very soon. But not quite yet. Drummond is a talented yet fundamentally unsound defender. But soon enough, he has a chance to be the best center in the league.
Roy Hibbert is really good. He probably deserves to win defensive player of the year. But Roy's dirty little secret is that his stats are simply...slightly above average. Hibbert has a 16.33 PER (behind the likes of Derrick Favors and Robin Lopez). Obviously, he's a lot more valuable than those guys, but he just does not excel enough statistically for his stellar defense to catapult him into the elite spot.
Al Jefferson...yeah right. Again, a horrendous defender. Perhaps the best low post scorer in the league amongst centers, but Jefferson's continual atrocities on defense cannot be ignored.
Nikola Pekovic is putting up another solid year that no one notices. The dude is a very good offensive player, and an average defender, and he's very scary looking. But he gets to play with Kevin Love. Joakim gets to play with Carlos Boozer.
Is Chris Bosh a center? Probably not on any team besides the Heat, but I guess he technically starts as one. I don't know, he's not really a center. Let's just not count Chris Bosh, k?
Now that I have shat on all the other good NBA centers Neil Funk style, let me wax poetic about Joakim for a bit. Mr. Noah has obviously had an incredible year statistically. But what we love about Joakim is all the things he does that do not show up in the box score. Sure, it is a cliché, but Joakim does so many things that aren't noticed by the simple-minded fan. For several years he has been an elite defender, completely unique in his ability to switch onto guards and wings and hold his own on defense. He's absolutely vital to the Bulls defensive schemes, and without him, our defense would fall apart (similar to how our offense has fallen apart without MVP D Rose).
But Joakim, incredibly, has become one of the best passing big men I have ever seen. The dude is racking up triple doubles like it's his job (wait, I guess that is his job). The Bulls literally run their offense through their center. A center who has almost no low post game. This is crazy, but Joakim makes it work.
Most important to the Bulls, and my argument, are those pesky intangibles. Chicago has witnessed Joakim grasp the leadership role for this team, as he's come so far from his goofy and ridiculous rookie season to his still goofy and ridiculous but strangely effective leadership style. It takes a special type of leader to keep his team tough and loose at the same time, and Joakim personifies the Bulls' style in such a unique way. Miraculously, this team is above .500, and it's mostly because of our All-Star. Is Joakim the best center in the NBA? I'm not sure. But is any center more valuable and absolutely essential to his team's success? Not this season. Congratulations, Mr. Noah.