They are the same company now, so they will have very similar standards. I would choose the one that has the routing you like best. A 12 hour layover in Detroit or only a 40 minute layover in Amsterdam are not worth saving $50 or $100.
As far as I know they are not the same company, they only cooperate as part of the Star Alliance.
Also wanted to add that I agree with previous posters: The routing of the flight is an important factor. Personally I try to avoid flights which have more than one stopover. And I prefer to have about 2 hours to get from one plane to the other as the airports where the stopovers take place are usually of the really huge variety and you never know how long it takes you to just walk from one gate to the other.
If you choose a flight that connects in the US, remember that at the first US airport where your transcontinental flight arrives you will have to go through immigration and customs. That might add an additional wait time (less for you than for me if you are a US citizen, those lines are shorter than for us foreigners
).
In Europe you will have to show your passport before entering the international part of the airport, but there usually are no long lines at all for the exit passport control.
However, be prepared that you will have to go through additional security screening before boarding the flight to the US as well as after arriving in the US.
Personally, I never had a problem with a 2 hour layover. However, if you connect in Munich on a Lufthansa or United flight, 1 hour will be totally fine. This is the airport with the best design ever for connecting flights. But it is also a very nice airport with some cute Bavarian souvenir shops - so a nice place to actually spend some time while waiting for your connection!