Could you estimate the total number of miles each year you fly on LH and on UA and which booking classes you purchase? The earning rates for the various booking classes differ between LH and UA. The miles that count toward status also differ especially for high fare coach (Y B), business, and first. In addition the cost in miles to redeem also differs between the programs.

Just to give you an idea here are the latest charts I could find for what you'd earn on your DEL-FRA-LAX LH flights credited to LH or UA (Europe has different earning rules). Things change from time to time especially for the lower fare classes.

Flying LH credited to LH
First Class A F earns 300%
Business Class C D J Z earns 200%
Economy Class B Y earns 150%
Economy Class G H K M Q V earns 100%
Economy Class L S U W earns 50%

A 25% status bonus (on base or reduced miles) is added for status holders.

Flying LH credited to UA
First Class A F earns 150%
Business Class C D J Z earns 125%
Business Class Z earns 100%
Economy Class B Y G H K M Q V L S U W earns 100%
Economy Class U earns 50%
Economy Class E earns zero

A 25% (for 2P) or 100% (for 1P and 1K) status bonus (on base or reduced miles) is added for status holders.

So you can see the earning structure and bonuses are rather different.

If you are buying economy on UA, that is basically going to credit at 100% to UA but if you credit those to LH the cheaper economy fares will only credit at 50%. Bonuses also work differently between the two carriers.

Then you can figure out what status you can attain on UA (e.g., 2P, 1P, 1K) and LH (e.g., FTL, SEN) and we can help you compare the benefits of the two choices.

Finally, you need to decide what you are looking for from your program: redemption of miles for trips in economy or premium cabins, lounge access on domestic and/or international itineraries, ability to upgrade flights.

Try this if you need to estimate mileage:

http://www.gcmap.com/dist?P=lax-del-fra