I don't know much about each breed as I haven't ever had one of either breed but I have been around both many times as my neighbor has a Maltese and my best friend has a Lhasa. Neither breed is really good with kids I don't know if that is of concern to you. The shih tzu's are very similar to Lhasa's but they aren't as crazy lol and they aren't as bitey. I have a male shih tzu and he is a great lap dog. He will be 2 June 26th. They are also a little bigger and sturdier. Be sure to research the breeder and see the room they are being kept in. Ask for references etc. If they have a problem giving you any information there is usually a reason for it in my opinion. The Maltese can be very high strung from what I have observed.