It isn't just the size of the bird that distinguishes the British Robin from the American one. The British bird is cute and small with a distinctive shape. It's depicted on many British Christmas cards along with snow, but we rarely actually get snow in Britain at Christmas. It does not live in flocks, but instead has it's own territory along with it's mate.
However the American Robin's shape is similar to that of many birds and it's much larger. I was surprised to see many of them today in a garden I passed on the way to the library. It looked to me that they are not territorial.
Of course my preference for the British Robin, or more precisely the European Robin, is probably familiarity. If I had grown up with the American Robin I may prefer that one.