John,
Hi, to answer your question. MyHeritage is technically correct. You are a 60 cM match.
The reason for the difference is the Ancestry Timber Algorithm.
https://support.ancestry.com/s/article/How-Timber-Helps-You-Find-Meaningful-DNA-Matches?language=en_US As described this does some filtering, so that it is easier to find closer relatives. However, I am pretty convinced that it actually filters real matches.
I think this can be seen by the fact that using Ancestry Pro Tools, where someone has no shared matches without, suddenly you see lots when you use Pro Tools.
Ancestry has been shielding us from the complexity of DNA, if you go back 5 or 6 generations, most of us are from places where everyone was at leat distantly related to everyone else.
I have matches I can see are real but are at the 7 to 10 generation or more level.
You can argue about the philosophy of this, but personally I would like to be able to turn Timber off, and see the full picture. Which is effectively what you have done by copying your match data to MyHeritage.
Timber is great for the early stages and closer matches, but it is a filter. People saying you get false matches without MyHeritage are viewing the information through that Timber filter, so personally I feel they are not actually false, just further in the past than perhaps most people are interested in.
Personally I am interested in the fact that I can be pretty much certain of the fact that my ancestors came from sound Lincolnshire and the North East of Scotland. That is what all that extra data without Timber is telling me.
I hope this was not too mutch of a tome or rant!
As an update, this is quite informative also.
https://dna-explained.com/2022/05/12/ancestry-only-shows-shared-matches-of-20-cm-and-greater-what-that-means-why-it-matters/