Only book the codeshare if there's a significant enough (to you, definition of "significant" will vary to each person) price difference over booking the native flight codes. Price difference can happen if one carrier has sold out of a cheaper bucket while the other has not. Also from a surchage issue that I'll mention later.

Otherwise what mahasamatman said. There is definitely a disadvantage to booking a codeshare if you want to upgrade: if UA metal you can't request an upgrade until day of departure (well technically until it's open for OLCI because it's then in the UA Departure Management System with the native UA#), and if LH metal you aren't allowed to use a UA paper SWU at all (according to the rules; I don't know about the realilty). Miles are the same, it's the metal that matters in Mileage Plus and most other *A programs.

Jeesh, how many times has a variant of this come up this week alone? We should have a sticky about codeshares.

Now, in the specific case of USA-Germany flights with UA vs LH flight codes for the same metal: In many cases when booking via Orbitz, booking one of the TATL legs as a UA code and the other as an LH code lowers the total cost. I believe that one of the fuel surcharges gets dropped. This won't last forever, and may not even still be there, but I've seen it many times. It doesn't seem to matter whether it's UA metal or LH metal; what matters to the pricing is that one leg is coded UA and the other leg coded as LH. Both legs can be UA metal, both can be LH metal, the LH coded leg can be UA or LH operated, the UA coded leg be LH or UA operated, it's just the mix of carrier codes.

This can NOT be booked on .bomb ever since the 2006-07 redesign which eliminated the ability to specify exact desired *A carriers. I think it has only worked on Orbitz, but I could be wrong and maybe other sites might also work. I'd expect if it still works on Orbitz it probably also works on Cheaptickets.com which is Orbitz with different colors and logos.