I don't know the for-sure answer, but I can make an educated guess.

ORD has its own fixes for traffic going east -- EBAKE, DUFEE, MOBLE, while MDW's go over LEWKE. Westbound ORD departures also go in their own tracks over IOW, PLL, MZV, and BDF (usually a 270 heading). MDW's go on their own track south of the ORD departure tracks.

In both of these cases, everyone is pretty much separated by the tower, and there aren't really many conflicts -- so go fast.

On the other hand, ORD and MDW share all 5 southbound fixes (7 if you count EON and RBS). In the TRACON, the ORD departures climb to 15,000 before going to Chicago Center, and MDW departures climb to 12,000, remaining underneath the ORD departures. I am going to guess that the 250 kt restriction (which applies to MDW departures as well as ORD departures) is meant to make it easier for ZAU to blend all of the departures together -- they can tell some to go faster sooner to help build their spacing into what they need.

I've seen ORD have 3 departures over EARND in a row, while MDW has 2 over EARND at the same time, so the center ends up with 5 airplanes at the same fix, all within 12 or 14 miles -- so having the option to speed 1 up at a time is probably a better than having to slow guys climbing out to make the space (especially since zig-zagging isn't an option because of DENNT departures to the west and BEARZ/LOOTH arrivals to the east).