very nice question

really fun
i personally i have trained many years in boxing and also trained some other things and analyzed martial arts and sports over the years and here is how it is :
in a 1 vs 1 situation boxer vs wrestler . no rules . the wrestler will win 90 or rather 99 even out of 100 . the only way for the boxer to win is to either knock the wrestler out quickly before he gets him (which will rarely be succesful ) OR if the boxer somehow achieves a groin kick / punch or eye poke or something like that ...either before the grappling starts or while the grappling . but this is unlikely to happen anyway because the wrestler will control the boxers
hands and feet with his wrestling skills
as soon as the wrestler grabs the boxer it is most likely over for the boxer . and closing the gap/distance is far easier than holding the distance (with punches and footwork)
however boxing is a very effective combat sport and a good sport to defend yourself on the street . one of the best actually . and is also an important part of MMA
and when you are on the street you should try to avoid to go to the ground because it is dangerous since your opponents friends can come and kick your head off or even stab you etc. while you are down
but year wrestler vs boxer 1vs1 the wrestler takes it most of the time