I would think you could call the draw cycle about the same considering they use the same cam/idler configuration...

. However, the Justice is about 2 to 2.5 inches shorter than the Liberty but with a brace height about a half inch larger. The result is a speed difference of about 6 fps in favor of the Liberty.
Those figures are off the top of my head. I may be a tad off here and there but not by much.