wow..those are some tight connections. Strictly in my opinion and experiences, I think both choices are simply too close. And this opinion includes that you only have carry-on luggage (I cannot imagine checked luggage making those transfers). I think the biggest issue is that, if you miss the LHR flight -- you are automatically staying overnight, and losing at least, what, a day? If there is anyway you get get to ORD or DFW earlier to make the LHR flights--I'd do that. I guess if you went via ORD, if you missed the LHR flight that night, you can catch the next morning's LHR non stop.

At DFW, the taxi time alone from the west rwy complex to (possibly) the east parking gates could alone take 30 minutes..and at ORD, an air traffic control ground delay program could easily eat up that already tight connection time. At DFW, the LHR flights depart from D gates--if you park at A, B gates, that could take up to 20 mins to take the train to D gates.

If you miss either LHR flight, you are stuck overnight -- that would be my biggest worry. Either way, I hope all works out just fine.