I don't have a clue about Bichon's. I've learned a bit about Lhasa Apso and Shih Tzu as my dog is a cross of the two breeds. IMO Lhasa Apso's a loyal, inteligent dog. You need to train them from a very early age and they can be good with children, unlike my one. Their barking's very strong but yet again they are very sensitive to very loud voices/noises (if we have a party at home my one just hides away in a quiet room). They can become depressive if exposed to extremly loud noises. If trained well they can become very obedient but with loads of patience. It can take a while to house train them. Lhasa apso's can become quite indipendent and they also can be wary of strangers.

The Shih tzu's a very inteligent dog too, they can become independent too. Hard to house train. They love to please. With loads of training and patience they can become quite obedient. They are affectionate, plkayful and very good with kids and other dogs. Just like Lhas apso they're too wary of strangers. Shih tzu's can have more health problems than Lhasa apso's. Both breeds need a regular hair brushing as their hair can get knotted up very easily. And with the Shih Tzu's you need to clean their eyes quite reguraly. They're both lapdogs and they love lots of cuddling and loving.