My wife says she can always tell where I am in the house because she follows the crumbs like I'm Hansel and Gretel. I am an excessively neat person, though. I put things away. Everything in our house has its proper place, and I can't walk by a stack of magazines without squaring the corners. This frustrates my wife to no end. As she sees it, for someone so particular about straightening up and clearing clutter, I ought to be able to swing a broom around every once in a while.
Instead of arguing about who cleans when and who puts away what, we've worked out a division of labor for chores. She is as compulsive about getting on her hands and knees to scrub the floor as I am about climbing behind the furniture to find every last one of the Legos and Hotwheels. In my case, the neatness fetish extends to other chores that involve putting thing in their proper place: taking out the trash, emptying the dishwasher, etc. Rather than fighting about the things we do poorly around the house, we make the best of what each of us does well.
Chances are, your partner is one or the other, the cleaner or the declutterer. Figure out which he is and put it to use instead of finding fault with what he doesn't do.
Get some help picking up the groceries, the kids...