Doesn't seem like you can have one without the other. The reason Bridge appears "inconsistent" is because he spends so much time "protecting the football and minimizing mistakes". He's not a gunslinger like Drew, he's tentative, and that frustrates the hell out of aggressive defenses. Especially early in games.
I've been fascinated by the contrast between Drew and Bridgewater's styles of play. He has been "perfect" in his own way. He'll never serve up a 40 burger like Brees, but he can keep the chains moving and win games. I wonder if there's any chance we would rotate QBs so Drew can come in when we need some quick strikes and Teddy could come in when we need to grind out clock?