I have AA EXP and LH SEN and find it useful to have both. I do the vast majority of my flying on AA, which I find to be generous and flexible, at least for the type of flying and places I usually go. UPG'd on 99.99999% of my AA domestic segments, even when UPG's were scarce. International UPG's at 100% the past 18 months, including UPG'd at time of reservation for most flights, with only a few where I needed to wait until airport checkin.

LH, on the other hand, has been extremely generous, with 1000 miles/segment minimums and 25% bonuses that were multiplied by the COS bonus. That all comes to an end on 8/1, though still a very generous mile earning program. The benefit I use the most is unlimited RCC and *A lounge access, as long as I am flying a *A carrier. This works for domestic or international segments.

I have not seen any problem getting awards on either program.

A lot depends on your needs, where you are going and the type of fares you buy. I usually buy the lowest available fare and UPG that. AA is the most generous for this type of flying. LH I have used for some of the deep discounted FC fares that were out there, as LH is much more generous (pre 8/1 as they are changing.) With all of the codeshare arrangements, you can go almost anywhere on either program, just not UPG'd on AA codeshares.