If you're moving to the US, one big advantage of having status on two airlines in the same alliance is lounge access. None of the major US carriers gives lounge access to their own elites (with the exception of Delta, for top-tier Platinum Medallions). You need to pay more than $300 per year, or have mid-tier status on a foreign airline in the alliance, to get into the lounges when flying domestically.

But if you have, say, Senator status on Lufthansa and United Premier Executive status, both Star Alliance Gold, you can credit the miles to UA and upgrade, but use your LH status to access the United Red Carpet Club.