I'm not a "senior ba" but I work with a lot of them in the health care space.  In no particular order this is what separates them from me.  

Again this is my opinion.......

Strong understanding of the business and the key drivers.  

Strong understanding of the particular unit you are with.  Marketing, Sales, Finance, Procurement etc.

SQL, the ability to look at data and build reports.  If you can't measure it, it doesn't exist.  

VBA and .Net are VERY nice to have.  You can build tools and other front end items to assist.  I build access front ends using VBA and SQL on the back end and this is very advantagous for our team.  I get noticed for it, which is nice and it keeps me from doing operational type work.  Some of our other BA's are very functional and get by just with industry experience.  

If you want to move into solutions or other enterprise level positions UML and TOGAF or some enterprise framework would be wise.  Very rarely do I see a BA certification required, but on really senior level positions I see UML and TOGAF (the certification) required.