For me:
Pro 05: 1356Hz, 85.0g, 5.9mm. Inner KLC, Limba top
Pro 01: 88.8g. 1485Hz. 5.8mm. Outer ALC, Koto top
They are different blades, you really need to know whether you want a Koto (harder) or Limba (softer) top, and whether you want the direct lower dwell time feeling of the outer carbon relative to the better control of the inner KLC (my feeling). I get more spin out of the Pro 05 with the same (new H3 Neo unboosted) rubbers.
Basically, the Pro 05 is closer to a 7-ply limba top blade like the Yinhe 437 or Yinhe U1-VB, or the Tibhar Samsonov Black Edition. The Pro 01 is closer to any of the other external carbon blades like the Yinhe T7S, T8S, (Cypress top).
Also I think the best rubber for the Pro 01 and 05 is the F/H DHS H3 Neo (or maybe Yinhe Big Dipper) and for the backhand it depends on how jumpy and fast you want it. I want it slow so I would play the H3 Neo if it weren't as heavy, so I play the Neottek Hinomi M or Yinhe Moon soft.