I don't see any way that either of them can be a heel, so it'll have to be a "mutual respect" storyline between two babyfaces whose paths are finally crossing.
Sting as the Crow character all through the build, speaking only enough to get across why he's there (he's coming to the end of his career and this is his last chance to do the one thing he's never done: end the streak). Showing Taker respect, showing Taker's fans respect, but leaving no doubt he's there to win and emphasizing that this is his last hurrah.
Mostly he'd be silent, totally serious, never smiling, hanging out in the rafters, occasionally showing up in the ring when the lights go out, pointing his black bat at Taker but never attacking him with it, and leaving Taker looking concerned and worried after every encounter.
I wouldn't have either of them wrestle at all during the build, and they wouldn't have any physical contact. 100% psychological storyline with Sting dominating.
As for the match itself, of course Taker wins in the end, but the match is heavy on storytelling and psychology more than action. And they show respect for each other and shake hands when it's over.
Gotta be something like that, right?