I think it depends on what we are comparing. There are four things we might compare:
1. The actual DNA results. These will vary a little because different companies test different parts of the genome and different amounts of the genome, but basically the results will be very similar. We don't usually get to see this data, it is a long file of As, Cs, Gs and Ts which is pretty meaningless to us.
2. How much DNA we have in common with other people who have tested. There may be slightly larger differences here between companies, partly because of the different amount of DNA tested, but also because some companies make up for the fact that they aren't sampling at as many points by (if I understand it correctly) "imputing" data that isn't actually tested, but which is statistically likely. I tested with FTDNA and Ancestry and my results here were very similar, only minor differences.
3. Then there is the prediction of the likely relationship between us and our matches. This varies even more between companies because of the differences in #1 and #2, but also because the different companies use different methods to estimate relationships. There is no "right" and "wrong" here because this is still an evolving science, though it would be interesting to see data on how each company predicts relationships that are known. Overall, I have found FTDNA to get this pretty right in a number of cases I can check, and Ancestry did OK too in the few cases there that I could check.
4. Finally, there are the ethnicity estimates. This is where the variation between companies is likely to be greatest because, again, they all use slightly different algorithms to calculate ethnicity. Again, there is no "right" answer, especially as our ancestors may have come from UK 5 generations ago, but Finland 15 generations ago and Ukraine 100 generations ago (as seems to have been the case with my mtDNA). And of course back 5-10 generations, we might have hundreds of ancestors, and they might come from all over the place, making assessment even harder. Everyone (except maybe Ancestry's TV ads) will tell you ethnicity is reasonably accurate at the continent level, but still not very reliable at the country or regional level.
So we should expect #1 and #2 to be pretty accurate, #3 to vary a little and #4 to vary a lot.
