Under the new rules ships have a handling rating. This rating is derived in ship construction from the amount of engine spaces a ship has. If you are are conducting a narrative chase, then use the handling ratings to determine the relative speeds of the ships. If the chase is using the combat rules then simply use the maneuvers as suggested above. After all ships in space don't really have speeds, just accellerations. Although the galaxy guide did put top speeds on ships due to micrometeor collisions and stress on the ships hull, but that varied by race not by ship.
While the ship construction rules provide a method for determining the handling rating, the ships in Ships of the Galaxy don't follow those rules. Many of them have ratings twice or more above what the rules say you can have. I reconcile this by adding a new ship quality called Improved Handling, and just use that as a catchall for why some ships break the rules. It also allows me to design ships that exceed the limits of the ship construction rules.