I was in the same situation. AA EXP and LH *Gold. Gave up on collecting on AA (lifetime Plat anyhow) and concentrating on Star and the LH program now.

Star has a few advantages: higher baggage limits (consistent on all airlines), good airports to connect like ZRH, MUC, CPH, DUS. (FRA is not much better than LHR) The LH program is good when you fly in paid F or C, the UA program is better for paid Econ because of the mileage bonus and the SWUs.

Also i find the award availability in premium classes far better on Star than on OW (limited mostly to AA and IB US to Europe).