Thrusting up will mimic centripetal acceleration, allowing you to maintain you speed better allowing you to stay in the blue zone more easily. However, if the opponent is very close and moves "up" from your point of view, they can easily travel outside your field of view.
Thrusting down will mimic "keep travelling in the same direction while you turn your ship" - almost like FA off. It tends to get you pointing at the target sooner, but you end up bleeding off all your speed (and going into reverse even!). Your ship will be sluggish until you get back into the blue zone.
Use a mixture of the two depending on the situation!