In the photo, the guy with no facial hair has boyish cuteness - he looks younger than his age. I think his disorganized hair actually helps with his younger look, and I'd guess he uses that to go after college age girls.
The facial hair of the other guy (you?) confuses me. The term "neckbeard" refers to hair attached to the neck - what do you think of cleaning that up? Maybe sideburns could be trimmed as well. Would you agree those changes give you a neater appearance?
When I've had a goatee, I've kept the sides trimmed in a striaght line so it looks neat. You could do that, or choose a clean shaven look (no goatee, no neckbeard, no sideburns). I'd suggest you try something different with facial hair, which you can always grow back later, to see if that helps you compete with your friend.