The nipping structure is the same
Noope !
I l o v e to notice that two knots are the same, when people believe that they differ - because I want to understand how knots, in general, "work", and why, so when I find a real, s t r u c t u r a l similarity, hidden under misleading, skin-deep "formal" appearances, I believe I do something potentially useful. So, to pop out and shout : "It is different !"" It is different !", is not my cup of tea - but when I have to do it, I do it.
See the attached pictures, of your Med. bowline II ( let us call it like this, for the moment ).
First thing one should notice, and admire, is the most beautiful side #1, where there is this LOVELY 3-symmetry ! This is a GREAT advantage regarding how easy is to inspect this knot - and it underlines that symmetry is not useful only regarding the structure of a knot ( because it distributes forces and stresses evenly ), but also regarding how easily it can be tied correctly.
Second thing is to notice that the areas where the double-line continuation of the Standing End = the double-line Standing Part before the eye = the double-line "nipping structure", approaches itself, are more than one. If it approaches itself only once, at one "point", we have a nipping loop. If it approaches itself two times, at two "points", we have a crossing knot.
At your knot, as it is dressed in the pictures I had commented on, it approaches itself two times - the second is shown with the two red arrows in the B&W picture. That is why I said it is not looking as a double-line "bowline" any more. It is not the topology of the nipping structure different than it was in the original Med. bowline, it is the geometry, and that is why I had claimed that the two nipping structures are different.
P.S. Perhaps we could say that the Med.II bowline is the "Eskimo" version of the Med.I ? ? ? I am not sure that this is not a far-fetched "similarity", nor that it is useful...