I own both. The Biewers in our bloodline (from Darling and Fru-Fru von Friedheck) are extremely attentive to their owner's moods, and they don't have a strong prey drive at all. This means that they would rather keep you company than run and chase a ball, although they love that too.
My Biewers are also more docile and less highly strung than the Yorkies. I personally prefer this over Yorkies because they are easier to handle, and they are just a joy to have around. When I'm upset, my little male will come and sit next to me and put his paw on my leg. My Yorkies are much too independent for such behaviour
I love both, but I'm a Biewer breeder, so I guess I'm biased
These are my Biewer babies:
Solange d'Orio Biewers