Beware.
You may want to see this about the nanoVNA (starting @ 2:05):
I already seen that. I think this is pretty normal behavior. In my opinion the root of cause for that is the common mode current on the outer braid of coax cable, because he uses unbalanced antenna with no RF choke.
Different VNA have different ground, for example one has bigger metal case, another has smaller metal case. When you connect antenna to VNA with no RF choke, your VNA metal case will be a part of antenna. So, the antenna parameters will depends on metal case size and geometry.
In order to avoid that, he needs to use RF choke. I think with RF choke on coax cable he will get the same results on both VNA