To answer your question: Yes, you should not run xcache and Zend Opcache at the same time. If you do, you'll get undefined behaviours, most notably "cannot redeclare class XYZ" fatal errors. That happened to me after a systems upgrade, where the packet maintainer activated Zend Opcache along the already existing xcache installation.
As for the matter of which of both to use for opcaching, that depends on your specific code - I'd recommend setting up a test environment and firing up the Apache Benchmark or a similar tool to check the answer times.
On a default wordpress installation, I was able to get a speedup (uncached vs xcache) of about 5-7x, which is quite significant. If you really need more, you'll need to check out the other possibilities already mentioned in the comments like
- using a loadbalancer and multiple application servers
- using memcache or memcached to cache database queries and other load heavy operations
- switching to another database system like a NoSQL system (be careful of the consequences)
- changing your architecture to a static site with webservices providing interactive content