How do you even make this debate?
Each character is different..
I'm guessing we're going with the implied characteristics by their surroundings to assume what each is like.
The Lone Wanderer is smart (son of a doctor, defused a nuclear bomb, figured out Project Purity's pass, escaped Trainquility Lane) and has been using guns since he was 10 (high perception and agility), but he was a bullied outcast in the vault (low charisma) prone to having everyone he knows and loves die (horribad luck). There's nothing to suggest he has outstanding strength or endurance, but we can assume his endurance is at least decent. The surroundings seem to imply that the Lone Wanderer is good at Medicine, Science (thanks to his dad and to them being commonly required in quests, small guns (knows how to use them since childhood), big guns (game just asks you to take and use that Fat man), and energy weapons (once the enclave arrives, it's all you ever see. Plus we have Mothership Zeta.), though it can be assumed he's good at a lot of things, considering his high intelligence. I'd say his SPECIAL looks like this:
3
9
5
3
9
9
2
(plus one to all of these thanks to bobbleheads)
The Courier is a tough son of a [censored] that survived two bullets to the head at point blank range (outstanding endurance) and not only that, woke up to find himself in the EXACT perfect position to get every major faction to kiss his ass, and the EXACT perfect position to take Vegas for himself. (outstanding luck) He also seems to have a way with words as no one gets anywhere without charm in Vegas and the Courier is personally sent by the major factions to negotiate and offer alliances to various groups (high charisma). The entire cowboy theme overtone seems to also suggest that he's quick with his guns. (good agility) However, there's really no reason to assume outstanding intelligence from him as he's constantly giving the option to say "wtf are you talking about" when the convo reaches a new level of intelligence, but there's also no reason to assume complete stupidity. Strength and Perception, we're never given any reason to believe they're outstanding, so they're also par or sub-par.
As for skills, the Courier would have to be as smooth talking as Benny (Speech and Merchantile), as good with guns as the NCR (small guns and maybe repair), and as dangerous and self-sufficient as the Legion (Unarmed and survival).
I'd see his SPECIAL looking something like this:
3
3
9
7
4
5
9
(+1 to all thanks to implants)
The only part I'm not sure of in there is why 7 charisma and 5 agility and not 6 for both. I chose that because while the need for charisma is obvious (Speech checks. Speech checks EVERYWHERE), the implications that he has agility are subtle (cowboy theme overtones the entire game, but no NPC comments calling the Courier quick with his hands or an exceptional amount of Agility checks).
Having said that, it might also be worth noting that the Courier is very likely followed by the Mysterious Stranger and Lady Luck. The Lone Wanderer is not.