I think Cox will be remembered by many as the most successful, unsuccessful manager in MLB History. Granted, had the Braves had the success of the 1990s here in this decade (at least making the LCS more than once) or one a World Series or two more (Although if Lonnie Smith had been paying attention, Cox has two WS rings) he'd be remembered a lot more successful by many more.
I think Cox does not get a lot of credit for managing the everyday team through 14 straight years. Granted its a lot easier throwing Smoltz, Maddux and Glavine for three of five days for so many years. But, how many times has it been seen that the Braves will sign someone on a whim, and once in Cox's system they give some positive production towards the team. So many times a guy like John Burkett, Chris Hammond or Jaret Wright have been signed to an almost nothing contract with a DOA career and have been able to flourish in the Atlanta franchise and been able to rob a team in free agency after leaving the Braves.
That goes hand-in-hand with dealing with a shrinking budget from owners Time Warner in recent years. The Braves and John Schuerloz would see guys walk away in free agency and either make a signing of a Burkett or Wright or pull the trigger on a trade to get an established veteran for one of their prized prospects - only to see that prospect flounder in his new home. Of course, all of this is due to the way that the Braves put things together top to bottom from Cox and John Schuerloz to the scouting and front office - they established a plan back in the late 1980s and its got them this far. A lesson for perhaps owners in today's game that change plans every 2-3 years like the Cubs, and some clubs that get it like the Milwaukee Brewers.
Then I think the fact that the cohesiveness of the Braves clubhouse is perhaps the best aspect of Bobby Cox. Very rarely has anyone not fit in or been trouble in Atlanta. The few instances I can think of involve guys like Jason Marquis and Tim Spooneybarger. Drama Queens Gary Sheffield, JD Drew, Deion Sanders and even John Rocker to a point (not-withstanding his relationship with Randall Simon) have fit in well in Atlanta.
And that nature of the clubhouse and how Cox treats his players - standing up for them, not lashing out at them through the media, and keeping with a guy who's 2 for his last 40 is what makes him a great manager and is what has made the Braves successful throughout the last nearly 20 years. It's also led to his ejections; if any player on the team gets tossed or even argues a call, you can bet Bobby will be making an early exit that day, its like clockwork.