Consider this: an unmanned missile can accelerate much faster than a manned spacecraft, so it can evade laser fire much more effectively as it approaches the enemy. At a critical distance it launches its payload: hundreds or thousands of tiny (e.g. 10 gram or so) fragments distributed in a grid (at a density of, say, 1/m^2 distributed over as much as a km^2 at the interception distance). These intercept the target at 10s, 100s, or 1000s of km/s. Such a weapon is hard to defend against, even with highly effective lasers, and is devastating to the target.
I would imagine that depends a lot on what the distance is. Release too close and you get blown up by a laser before you can release. Release too far and by the time they get there the ship will have moved away.
I don't mean the big missile, I mean the payload that InclinedPlane's strategy described - a missile shooting out a few thousand mininukes a short distance away. Such small payloads, even if we give them engines (which also makes them shine brightly to anti-missile lasers) are simply too small to outrun a ship - small engines tend to be very inefficient and slow.
