I think you should go deep, but not with a certain technology. Think about it a bit differently and go deep in an area.

For example, as you put it, instead of being "the best SQL guy" work your way on being "The best Database guy". Instead of being "The best Javascript guy", go towards being "The best Frontend" guy.

Remember, technologies change fast, there will always be new platforms, new DB types (just think about Big Data and their adoption rate in the latest years). You will not be safe if you master a technology, but if you master a domain you will have deep knowledge on the subject and you will be quick(er) to adapt to any new technology coming your way.

Best of luck!