I'm missing these menu items "Quick Fix" and "Create JSF2 composite..." from Context Menu of Source pane of VPE containing XHTML page when SWT Bot tests are run via maven.

Most probably a missing dependency, or a SWTBot bug with Eclipse 4.2...

Maven command: mvn clean install -P default,jbosstools-staging-aggregate -Dswtbot.test.skip=false -Dmaven.test.failure.ignore=true
[...]
Any ideas how to find out what went wrong?

When in such trouble I do run "mvn verify [blah] -DdebugPort=8000" and configure a new Remote Java Application Debug configuration in Eclipse that listen to JVM on port 8000. Then put a breakpoint on your test before it fails, SWTBot thread gets suspended and you can play with Eclipse UI.
When test is suspended, verify manually on the test instance whether this menu is here or not.
If you can see the menu, it's an SWTBot bug, if you can't it's a target-platform bug. Use Plug-in Spy on a working Eclipse to see which plugin contributes this menu and verify the contributing plugin is a dependency for your SWTBot test.

HTH.