Ok, IMHO "spillting up" if thats kinda like what you are doing is a stretch if this is a girl you could end up spending the rest of your life with. If you both feel like you could eventually get married, the last thing you want is both of you going your own way every time you get into an argument. When me and my wife argue about stupid crap (and it gets intense sometimes), we walk away from each other and avoid any verbal communication for a couple of hours, this gives us time to cool off and just think about everything.

I guess what I am trying to say is, it all depends on how you two really feel about each other, if it could become very serious, then work it out, but if you feel that you or her could just end the relationship at any time, its not worth either one of your time.