I disagree with most of the posters. If I am traveling from either ORD or MDW to the Loop with a person with limited mobility (and I occasionally fall into that category), I would say that you should take a shuttle or taxi into the city.

At Midway, you are going to have to drag your bags about 0.4 miles to the Orange Line. Quite often, the elevators/escalators that take you to the street level are NOT working. Also. once you get to the Loop on the Orange Line, it can be a real PITA to get to the elevator (which also on occasion does not work). Your best bet is the State/Lake station.

At O'Hare, depending on the terminal, your walk to the transit center can actually be LONGER than at Midway (yes, I have measured it). Generally, though, the escalators/elevators and the walking area is all inside which makes it a lot easier. However, the Blue Line is under construction and at some points, you will be bussed from the airport to the Rosemont station. Also, much of the Blue Line is under construction and there are two LONG "slow zones" between O'Hare and the Loop that stretches a 40 minute ride to the Loop to as long as 70 minutes (on occasion).

If you were doing this at rush hour, avoid the trains as they are packed and there is not a lot of room for the luggage.