Are you only choosing between those two breeds? I have very bad allergies but, have had no problems with my maltese. Malteses look similar to Bichons. If I were choosing only between a bichon and shih tzu, I would choose bichon. Poodles, bichons and malteses are the top three choices for people with allergies. (I still say go for the maltese though!)I just cannot make up my mind! We have three kids (9 year old twins and an 8 year old), one of whom has allergies, so that is an important consideration. Any thoughts or advice would be greatly appreciated!