who would win

Well that would depend on their character build but my guess is that with the overpowered VATS and Iron Sights the Courier has a leg up in the gunplay department. But, the Lone Wanderer would just have to wear some sort of orange camo suit and the Courier wouldnt notice him. Although the lone wanderer does have more perks and probably would have some serious firepower at this back with the full support of the BoS.

Wanderer.

They'd both die in an explosion of biblical proportions.

Wanderer is a wuss, The Courier would kick his ass all the way back to his daddy...oh wait.

It would be a tie. I made them....... They are both sooooo unbelievable that they would agree to disagree and go about their day.

They'd unlesh mass destruction upon the world as an unstoppable force collided with an immovable object. Or they'd sleep together, assuming compatable sixual orientation.

As far as MY Courier and Wanderer match up, I would have to say my Courier. It would be a close match though. But my Courier is a Desert Ranger, and my Wanderer is a BoS Paladin. Desert Rangers > BoS.