Using CO as my primary carrier and UA as my secondary, I have to say I love CO. But I've also been a Platinum with them for the last nine years. Their service is great, they admit to their weaknesses and try to fix them and management has been particularly candid, especially with FTers with the presence of COInsider.
Domestic upgrades can be easy or hard, it's all a matter of routes. Transcon upgrades are rare, even as a Platinum unless you're on a full Y fare.
For me, it's always nice to go back to a CO flight after i've had an abusive relationship with UA, which seems to be increasing in frequency.
The one short-fall is international upgrades. There are no SWUs, at this point, you have to buy a full Y fare to upgrade without a "processing fee". Though, the flip side is you can upgrade any class with miles and a processing fee so you don't have to buy a certain fee, just pay the tax.
As for Asia, currently they code-share with NW out of the NRT hub. The only PacRim routes are EWR-NRT/HKG/PEK and IAH-NRT. EWR-PVG is coming in March. They also have EWR-BOM and EWR-DEL for Asia routes.
The European network is much more diverse then UA as CO serves a lot of the secondary cities as well.