Permissions required for running extended events
As Jonathan stated and the link shows CONTROL SERVER is required prior to SQL Server 2012 to create an Extended Event session. The ALTER ANY EVENT SESSION permission prior to SQL Server 2012 only allowed a user to start/stop a session, or change a current session; it will not allow them to create a session. CONTROL SERVER is required for that ability.

If this is a production system it is based on your company's policies but I would not provide a developer that level of access to anything in production. I would likely create a few different sessions that they might need for troubleshooting code in production, and then grant them ALTER ANY EVENT SESSION so they could run that as needed. They would also have the ability to then change the session as they see fit. However, be aware that even though Extended Events has less overhead than Profiler it still has overhead depending on what you are trying to capture. I would hope the developers have an understanding on what events can cause additional overhead.