My general answer to this kind of question on "efficiency" is almost always, which ever version of the code is most readable, is the most efficient.
That being said, I think (val.ToLowerCase() == "astringvalue")
is pretty understandable at a glance by most people.
The efficience I refer to is not necesseraly in the execution of the code but rather in the maintanance and generally readability of the code in question.