the beer is much better in Dusseldorf, and I think that walking in the old town and by the river is nicer. The cathedral in koln is pretty spectacular. dusseldorf has much better night life, and a better resterount area - more better places in a smaller area.
koln has a world class archeological museum and a very good art museum. dusseldorf has 3 or 4 very good art museums - if you like german art of the early 20th century, dusseldorf is the place. if you like antiquities, koln.
Dusseldorf also has a classy, cosmopolitan feeling.