Clearing order for complimentary upgrades (as space is available):
Traveling on United: United Global Service, 1K, and Premier Exec clear first, followed by Continental Platinum and Gold Elite.
Traveling on Continental: Continental Platinum Elite, followed by United Global Service and 1K, then Continental Gold and Silver members.
Continental just joined the Star Alliance program a few weeks ago but their relationship with United dates back to June 2008. Recently, for example, United announced Red Carpet Club members can now access the network of Continental President's Club lounges worldwide.