According to a comment on the HHVM blog, as of April 2014 there is no runtime difference due to the types being erased at runtime.
However, once that changes you should be able to expect a small performance increase, considering that HHVM is optimized for Hack, and that static typing is generally faster than dynamic typing.
And a little bit of background:
HHVM had to be developed from the ground up, and is still relatively new. Facebook's codebase was originally in PHP, and moved to Hack as they had time to recode. They are focusing on improving the runtime as a whole, and this is (comparatively) a very minor area of improvement. The change would only affect Hack, so I expect they will delay that until they are running low on other, larger improvements