Is single-source single-destination shortest path problem easier than its single-source all-destination counterpart?
Nope. In order to find the distance from $s$ to $t$ it is necessary to determine the length of all paths that are at least at the same distance as $t$ is. If $t$ has a "median" distance half of the distances will be known that way.

In certain application areas (with an exponentially sized "implicit" state space) it can still be worthwhile to start searching from both sides and look for nodes that are found in the middle.