With your EASA license you can only fly EASA registered aircraft. Nothing else. To fly aircraft from other countries you need to have your license validated by that states CAA or acquire their local license. With just a CPL + ATPL theory this is often very difficult or impossible. If you hold a full ATPL it is much more simple and straight forward.
The second issue is work permit which many people forget or confuse with the Flight Crew License. Take for example to vast amount of foreigners with FAA licenses. They are allowed to fly FAA N-registered aircraft and some might even do so in foreign countries. But because they have no right to live and work in the United States they cannot use their FAA license to work in the USA. They need a green card or employer sponsored working permit/Visa which is very difficult to get.
Regarding China it's like smiling monkey says. China produces vast amounts of local F/O both in China and in other countries to fill the right hand seat. Captains are more difficult to produce and that's why they have to look outside of China. They then look for people current on type and with Pilot in Command hours on that specific type. Something that could take a new pilot 10-15 years to acquire from starting pilot training.