I have a small scanner from AVID and it reads both AVID and Home Again Chips. The numbers are in different sequences, so you know which it is.
Then we got the free scanner from Banfield - that reads AVID, Home Again and Banfield chips - all 3.
I always used AVID chips, as they offered special pricing to shelters/rescues. But I have always offered to check existing chips in dogs who people brought along when they came to adopt -- and I've always offered free scanning if someone finds a dog.
That has given me an opportunity to find the other types of microchips and know for sure that the scanners do read them all.
They won't read the European chips, but that's not really an issue for me, in this area.