http://www.mangago.me/read-manga/ore_tachi_no_kijou_jitai/ probably not, because it's yaoi but it's also funny
http://www.mangago.me/read-manga/yume_ga_kanau_juunigatsu/mf/v01/c004/2/
Not the last story, but they do fight all the time and it's funny.
maybe: http://www.mangago.me/read-manga/blood_honey/
the last story
you breaking your brain into another elusive manga zephyr? seriously you create a list or album like "mangas i should remember or something" lol
anyway, here's the manga i do remember that greatly matches your description http://www.mangago.me/read-manga/relationship/
This request is quite difficult because I don't remember much....
It was the last chapter in the volume and probably not related to the main story at all (I didn't read the main story).
It was hella funny and was shounen-ai although the the manga itself was yaoi (get my point right?).
There are these two friends and they challenge each other so much and in literally everything. I remember them fighting (karate?) and what not (boxing?) but it was always a sort of tie or either one of them winning.
It was really funny....
I don't remember anything else.
Thank you.
Edit: found it. It's the last updated chapter of Access
http://www.mangago.me/read-manga/access/mf/v03/c000.2/2/
A very big thank you to all those who helped me find it. :)