Here's a good stackoverflow post on the topic (note this is about openjdk 7). Things have only improved since then.
https://stackoverflow.com/questions/11547458/what-is-the-dif...
If you are doing any kind of server side deployment, openjdk has been a drop in replacement since the java 7 days. Essentially all linux distributions include it and you have to jump through hoops to get the oracle version.
There are differences between different openjdk builds though. I've ran into issues with certificates a couple of times on Ubuntu. Also they had a strange notion of what is stable and what is not early in the life of java 8. Another issue is the licensing of the test suite. This makes it hard to test your builds. The words certified build, implies that the produced build passes the licensed test suite.
Most of the differences are commercial features you're not allowed to use without a commercial support contract with Oracle. The only other differences are so small you probably wouldn't notice.