Originally Posted by zoeper
...the alignment that is (automatically) controlled by the case and not the press, and that this results in less run-out.
There is enough latitude in the shell holder of a standard press that the case aligns itself to the die routinely. Some remove the wire retainer and replace it with a rubber O-ring to allay all doubt. The two critical elements are ram play (lack of) and die alignment. You won't go wrong with either press. It's a matter of evaluating the trade-offs (ergonomics and limitations) of the designs, and then deciding which really appeals to you.
As an aside, Glen Zediker, noted reloading and shooting guru, wanted a press for seating bullets at the range. He chose the cheapy Lee C-press. He floated the die in the frame, using rubber O-rings both under the die and to retain the shell-holder. That press with all of its slop and imprecision is the last one I would choose. He was perfectly satisfied with his run-out. He now represents Forster, but I doubt that he hauls a Co-Ax to the range (it probably just replaced his old Boss). He uses an aluminum turret for that purpose. I haven't said it, but perceived desirable results generally follow the choice of equipment, ruling out obviously poor choices or defects. People tend to be happy with what they buy, reinforcing their purchasing decision.
I use a Redding Boss and feel no need for anything else. If someone gets warm fuzzies from owning the Co-Ax then he knows what makes him happy. I would pay close attention to ergonomics; it's what you'll really be living with. But go with the one that makes you happiest; that's the most critical element.
The dies don't determine the desirability of neck turning. Having a tight-chamber barrel permits the fitting of the case neck to the chamber, and that requires neck turning. Many use the Lee collet die for factory barrels.
As a suggestion, you may want to obtain a copy of Zediker's book, Handloading for Competition
. It's available from Sinclair or Zediker directly. If you get it from Sinclair, you can request their catalog. Reading it before making a choice may make sense; you'll carry more information into that process. It's difficult to read due to Zediker's writing style, but also it's very informative.