Going to stick my oar in here.
These kind of printing problems can be very difficult identify and, sometimes, to rectify. It is always a process of elimination, to gradually eliminate everything that might be contributing to the differences until you are left with a conclusive cause. The task you face is made more challenging by the fact that there are many potential causes that can be the source of the differences you have noticed. Thus, it requires patience and a meticulous approach to remove each possible cause, one step at a time. But it is possible !
In essence you have to make sure that you have eliminated all possible differences between LR/PS and Aperture in the image to print chain so that none remain. Once you have done that then the cause will be something to do with a difference between Aperture and LR/PS.
So my suggestion is start with making sure that everything is the same between Aperture and LR/PS. You have already eliminated the image file itself as a possible cause since you have printed from two files with, I understand, the same result. Thus, you need to make sure that everything in Aperture and LR/PS are the same from the working colour space all the way down the printing chain to the final print coming out of the printer. This will include the Page Setup / Print dialogue settings, the print driver (have you got two printer drivers for your printer – Aperture using one and LR/PS the other – Check in the System Preferences 'Print & Scan'). And so on and so forth.
You will have to be very meticulous and make quite a lot of prints. I speak from experience here, having had to diagnose something similar for myself some years ago.
Good luck ! And, please, keep posting to this forum on your results.
