Some of my thoughts:
Natural setting: Kansas City is set in gently rolling hills and prairie. Cleveland's topography is a little bit flater, but there's the North Ridge, and Lake Erie right nearby. Winner: Cleveland
Economy: Kansas City is growing, and is the home to several Fortune 500 companies. Cleveland also has corporate headquarters, but its economy is less diverse than that of KCs. Cleveland has no real edge cities, either; they can be an indicator of the economic prosperity of a region. Winner: Kansas City
Downtown: Both cities have hurting downtowns, but Cleveland still has a vibrant theater district, the clubs and lofts of the Warehouse District, and the struggling yet still viable party scene down in the Flats. Cleveland also has retail in Tower City, and scattered throughout downtown. Downtown Kansas City has some limited loft development, but is otherwise a poster child for dead downtowns. Winner: Cleveland.
City proper: Kansas City has the Country Club Plaza, healthy middle-class and upper middle class neighborhoods, some gentrification, and tons of new development in the Northland. Cleveland doesn't have much of a middle class in the city limits; the East Side is still recovering from riots in the 1960s, and the West Side is still mostly working-class. Winner: Kansas City.
Suburbs: In Kansas City, the majority of suburbs either have a Denver/Phoenix-like planned community feel (Overland Park, Olathe, Leawood, Lenexa, Shawnee), or they're places where you can smell the meth cooking a mile away (Independence, Blue Springs, Raytown, KCK). Cleveland's suburbs, with the exception of the City of East Cleveland, are demographically all over the map, and they seem universally pleasant. There are nice urban suburbs (Cleveland Heights, Lakewood), upscale old-money towns (Shaker Heights, Rocky River), large estate communities (Pepper Pike, Hunting Valley, Kirtland Hills), comfy middle-middle towns (Lyndhurst, South Euclid, University Heights), new-money towns (Beachwood, Solon, Concord), and not-too-bad working class burgs (Euclid, Parma, Garfield Heights). There's ethnic variety; reform Jewish Beachwood, orthodox Jewish University Heights, Slavic Seven Hills, Italian Wickliffe, Italian and Jewish Lyndhurst, Polish Parma, African-American Warrensville Heights, gay Lakewood, integrated-and-proud-of-it Cleveland Heights and Shaker Heights. Winner: Cleveland.
Culture: Simply stated, Cleveland wipes the floor with Kansas City. Old money, old money culture, museums galore, lots of colleges and universities, and a huge cultural center around University Circle.
Recreation: Lake Erie, Metroparks, and skiing nearby versus ... uhh, the Ozarks are a few hours away. Cleveland.
Food: No need for discussion here ... Kansas City. Restaurants, BBQ ... the options are endless, and the quality is outstanding. Cleveland could do better.