(from the O'Hare Hilton business center)
You are probably a UA-Mileage-Plus member (and not a LH miles&more), are you?
After UA overdid all the transatlantic equipment (seats), I rate LH & UA qualitywise the same in business.
Upgrades: by principle, you can only upgrade (using miles, or international one/segment/upgrade/vouchers, or hope to be "voluntarily" upgraded at the gate, if Flight-number and actual carrier are the SAME. (ALL transatlantic/flights from LH and UA are code/share/flights, and with both carriers).
If you are only UA-mileage-plus-member (and not LH miles&more) you get your status/bonus (25% as Premier, 100% as PremEx) with both carriers on the transatlantic-segment but only with a UA/flight/number (but with difficultiers for correct credit atr the end .... but that's another story I reported extensively under the UA topic).