Not sure if you ever found answers but here's a link about Amrocks:
https://www.rightpet.com/Livestock-poultryDetail/amrock-chicken
As for Barred Rocks they and Dominiques were once considered the same breed except that around the turn of last century there was some quibbling about whether they should be standardized as SC or RC in the APA. The quibbling groups broke away from each other and the BR group registered as SC and the Dominique group was left to register as RC.
I have had both of these breeds and prefer the Doms over BRs. The BRs in their history have had other breeds like game and Malay crossbred into them to increase their body size to be more dual purpose and their personalities are a bit dominant in a flock and unpredictable ranging from mellow to aggressive whereas the Doms were left to breed naturally like their Colonial history more calm and less combative. Both are good foragers and the BRs are not just good layers but good for sizeable carcasses. The Doms are a bit lighter-weight and will have a tendency to brood their own young and be more economical on the feed bill. It's a gamble on what temperament you get with BRs because of their game bird cross-breeding and what line they come from where Doms have been consistent in their curious outgoing temperament and seem to actually crave human interaction - Doms are a chatty bunch if you talk with them. You'll always know which chick is the Dom in a brooder because as one breeder said - they'll be the chick running up to curiously watch you as you watch them.