In my personal opinion, the Patriot gets the nod in the looks department. The 2011 redesign did wonders for the Compass (at least in the pictures I've seen - 2011 vehicles will only be available in Finland in the fall), but it still looks more like any other CUV out there and less like a Jeep than the Patriot. And the older year model Compasses look just weird to me. But hey, that just me - some people prefer a Compass over a Patriot and there's nothing wrong with that.
The boxy design of the Patriot may make the rear hatch slightly better for loading large items in the cargo space.
The more aerodynamic design of the Compass may slightly improve its fuel economy?
But seriously, asking on a web forum which vehicle you should like more? You'd be much better off visiting dealerships, taking both the Patriot and Compass for test drives, and thinking things through for yourself. Or, just choose the one you get a better deal on.