Sorry to bump, but I have some crap to say, hat-wise.
I'd say the hat.... I think that's the closest thing we'll ever get to an actual, in-relative-proportion Mario hat.
I hate seeing normal baseball hats or trucker hats with a mesh back half on it with a huge white circle glued on it that has a generic, Arial font "M" printed on it. Also, I hate seeing people trying to pass off Newsboy caps with the brim button popped as a legitimate Mario hat.... Mario's hat isn't poofy or anything. (Although... the Newsboy I have is actually very close to the shape of Mario's hat, but does have a bunch of seams coming from the center button on top.
So yeah, I'd take the hat on account of not owning Punch-Out.