If Sting goes to WWE, TNA will simply do a Best Of Sting in TNA. That way with the inevitable best of Sting WWE will do fans, can buy the DVD sets from both companies for a complete retrospective on Sting's career if that's what they really want.
This is the best point made on this thread, kudos to Alex. TNA will cash in on the Sting phenomenon, especially if/when the WWE makes him a superstar again. Let me clarify, by saying that TNA did their best with Sting during his tenure with the company. TNA did a great job with Sting's character, and did a great job protecting his legacy. TNA also did a great job of making Sting relevant since his WCW departure...probably not as relevant as the WWE could or would have, but I don't think WWE would be as interested in signing Sting today had he only been wrestling for smaller companies (or making indie appearances, or not performing in the ring at all). Unfortunately for TNA, however, they weren't able to give Steve Borden as much exposure as the WWE will. I know, that's like saying chocolate tastes better than poo - but sometimes the obvious needs to be pointed out. Sting signing with the WWE will benefit TNA in that regard, in that they'll most likely sell more "Best of Sting" DVDs than if Sting re-ups his contract with TNA.
Back to Alex's point, my son absolutely adored Jeff Hardy during his last WWE run (as I'm sure most kids his age did at the time). Jacob (my son) was NOT a TNA fan at the time, but wanted every Jeff Hardy DVD available. In turn, he got a "Best of Jeff Hardy" DVD that TNA had released, which included footage from his first run in TNA. Jacob loved watching that DVD even more than anything the WWE released. Did it matter that the DVD was released by a different company? No, because the matches included his favorite wrestler. TNA also released a "best of" CM Punk DVD (or at least a digital version of such) during "The Summer of Punk", if I'm not mistaken. A lot of people give TNA guff for trying to "cash-in" on their video library in this fashion...but who wouldn't? A company would be idiotic not to, and TNA won't miss the chance to cash in on their library of Sting matches...they've got a lot of great ones, too.
Will a WWE "Best of Sting" DVD be "complete" without Sting's TNA matches? No, it won't...but TNA will make a damn fine "best of" compilation of Sting's TNA tenure, and it will be comparable to anything WWE would have done. It will no doubt be a great companion piece for any die-hard Sting fan, because it will (or at least should) include interviews with wrestlers that aren't WWE employees (guys like Angle, Samoa Joe, Abyss, Austin Aries, etc). Sting is obviously one of the most (if not THE most) respected wrestlers TNA has ever employed, hence him being the very first TNA Hall of Fame inductee. TNA will release a fantastic DVD of his post-WCW career, and that will complete anyone's needs for "the entire Sting enchilada".