Either way, the competition has to be local enough to stop you while you are still in the 'thinking' phase. It also doesn't do any good to launch a .95c shell of expansion if they can come by a million years later and launch a .99c shell. (With those exact numbers, we beat them to locations within 40,000 LY and they beat us to all other locations).

However, the best of both worlds is theoretically possible; launching a set of colony ships now does not preclude launching a faster set later. The first colonists out should just be warned to anticipate that they might not be the first ones to arrive.