It is exactly $2^{64}$. You need to look for all possible keys for a successful brute-force. One cannot guarantee that the key will be in the half, $2^{63}$, that you are going to search. In, CS there is an adversary argument, that the adversary can always force you to the worst case. Tell him how you the search, he will produce a case that you are not going to find in $2^{63}$ key-space.
Actually, $2^{63}$ is the average case that you will find your keys during the brute-force.