I think the Barred Plymouth Rock is probably the most popular breed for the small flock. It has an edge over the Rhode Island Red because Barred Plymouth Rocks are generally more friendly than Rhode Island Reds. But Rhode Island Reds are better layers.
Which breed is best for someone depends on what they want chickens for. Most people with backyard flocks want friendly chickens that are good layers. The Barred Plymouth Rock usually meets those requirements.
I would challenge that one, the part about RIRs being better layers. You really can't make a true blanket statement like that. A hen can't lay more than an egg per day (except maybe a very rare glitch). I have consistently had both RIRs and BRs and the BRs laid egg for egg as many as any of the RIRs, hatchery and breeder types included. I consider them equals in the egg laying department and I think you'll find many folks who have both breeds would agree.