I know plenty of students from Washburn and UMKC and I seriously doubt that either school could give the average student an edge. Washburn seems to have a more loyal alumni base in Eastern Kansas, but that's just based on people I know.
The job market in KC sucks right now, but It may be better in 3 or 4 years (who knows?). I know some very talented and highly ranked students from both UMKC and Washburn who are graduating in May without any prospects.
I'm fairly sure that KU has a pretty decent edge over UMKC and Washburn in Kansas City and Witchita, but Washburn probably competes pretty well for the limited number of jobs in Topeka.
PM me if you want me to put you in touch with some people.