I have heard about differences in perceived quality of PhD education in different countries meaning that some degrees may not result in employment if the institution doesn't view the other as at the same level. I have heard of this with, for example, those with degrees from African universities trying to get a job in the US and sometimes they may need to get a second PhD at a US (or equivalent) university. This is basically due to some schools having fewer resources or not teaching the material on the same level or in the same way. It may be a strong tendency rather than a rule. In fact, I would guess this is just a common result, that candidates with "better" degrees would be selected instead.
But I don't see any of this applying to Europe/US. The bigger issue would be having a compatible/relevant theoretical background that the institution wants.
I have heard, in fact, that a US PhD May offer better training thana European one, whereas a European undergraduate degree would be better than a US one. (I heard about this while planning where to go to college then grad school.)