I am asking about putting a new Shibata in an X-1IIe body. Will that be equivalent to a new Shibata in a X-1II body?
I have no ideal what do you mean and the logic behind this idea. If you like to buy a broken cartridges to make a Frankenstein then it’s up to you.
Re-tipped cartridge will never be even close to the original Victor Shibata/Beryllium. The X-1IIe does not have a Beryllium cantilever like the X-1II, when you will put new tip on different cantilever the sound will be different. Actually the whole re-tipping process of MM cartridges is such a BS. No one on this planet can offer Beryllium cantilever anymore, none of those re-tippers, they can't offer even titanium pipe.
The price for a NOS original boxed DT-x1IIe with ultra light and rigid Titanium Pipe cantilever and pressure fitter Nude Elliptical tip is no more than $400 (for an original).
What else you can get for that amount and where ? Normally this is what re-tippers charge just for the stylus tip (make no sense), but they can only glue the new tip to the existing cantilever or they can offer completely different cantilever, but they can’t do that on MM cartridge properly. Those victor have a tension wire inside the stylus assembly. Rebuild/Retip is just a waste of money for inferior technology. Look at the images of my Victor cartridges on macro lens and check how the stylus tip fixed to the Titanium or Beryllium cantilevers.
I've seen some third-party styli for X-1IIe with strange aluminum cantilevers, but they are junk compared to the original Victor styli.
IOW, what, if any, difference in the X-1II or X-1IIE cartridge internals.
You can download the manuals and compare the specs.
P.S. Best Victor cartridges in MINT condition with original styli cost money, they are extremely rare and very hard to find in perfect condition. Once you will be able to check the original you will understand why they are expensive.