Despite their small size the Maltese is a comparatively robust little dog who as long as they are well-bred and socialised, are active, friendly, trusting and alert. They bond very closely to their owners and will want to go everywhere with them.
The Shih Tzu
The Shih Tzu is an extroverted, confident, affectionate dog who can be quite independent and aloof with strangers. And while intelligent, sometimes the impression is that they think training is beneath them!
The Malshi is a small companion dog who will enjoy games - but will mostly enjoy being with their owner. The personality of a Malshi seems to be more consistent when they are first crosses (F1). As a line is successively bred, they can be either bred back to one of the original breeds (and so strengthen either the Maltese or the Shih Tzu personalities) or else be bred to another Malshi - in which case there is less predictability in temperament (and in-breeding becomes more of a potential issue).
Responsible breeders should be prioritising behaviour as highly as health and so it is important to find a good breeder. A well-bred Malshi should be outgoing and confident, not nervous, shy or fearful.