Hmmmmm, I had a few old games that didn't work on a Amiga 1200,
I managed to get around part of the problem by using Relokick or a degrader
I think I am right in saying that there ARE old games that won't work on a 1200.
As for the 600, to be honest I never had a problem with any games on my 600.
I am sure some of the more experienced guys on this forum will have many comments and suggestions