...far too often when CUP systems are used, the results are stated as PSI. There's quite a difference in actual pressure between them in the 50,000 CUP (60,000 PSI) range. Down in the 30,000 range for both, they're virtually identical. SAAMI specs for the .45-70 are 28,000 both CUP and PSI...
While both CUP and PSI are used to specify allowable pressures, they measure those pressures very differently and it's not possible to make accurate general assessments how they will relate to each other beyond the very broad, and not very useful, statement that a as CUP figures increase, PSI figures will also generally increase and vice versa.
Dr. Oehler did an extensive analysis of this topic and his assessment was that "...there is no way to predict CUP from a peak PSI reading, and there is no way to predict a peak PSI reading from a CUP reading."
It's not a good idea to assume, in the general case, that CUP and PSI figures will be "virtually identical" based simply on the pressure range that the cartridge fits into, e.g. under 30KPSI.
For example, the .44Special has a CUP rating of 14,000 but a PSI rating of 15,900 and the .45ACP has a CUP rating of 18,000 with a PSI rating of 21,000 even though both cartridges are well under the 30KPSI limit.