This answer gives a pretty unintuitive result. Apparently, acelerating at a constant rate without a speed limit takes longer (from the frame of reference of the traveler) than accelerating with one. I think it's unintuitive partly because it seems like accelerating for a shorter time would require less energy, and therefore should not be able propel you a given distance faster. But, while the power required to sustain constant acceleration in a Newtonian model is constant, that's not the case for a relatavistic model correct?
Obviously, despite my intuition, it's not valid to compare enegy requirements across different models, but I still think it's an interesting question. In which model, newtonian or relativistic, would it take more energy, $E$, to travel a distance, $d$ (from a frame of reference at rest), while accelerating with constant acceleration, $a$ (from the frame of reference of the traveler), starting from rest?