What is the best brand for ductless mini-split HVAC system?

Our recommendation to find the best ductless mini split heat pump is not as much to point you to a brand but to help you know what to look for. Learn about heat pumps here –

Choosing the best minisplit heat pump for efficient heating and cooling

Technology changes fast, and we aren’t married to any particular brands no matter what the product category you are talking about. We have used a few brands of heat pumps in our builds, one of which being Mitsubishi that you mentioned. Heat pump performance has greatly improved over the last decade, and the biggest improvement comes from their lowest operational temperature.  

Heat pumps in the past used to only function well to about 14°F or -10°C . The better brands of heat pump available today can still function down close to -22°F or -30°C, though the efficiency falls off the colder the exterior air temperature gets.

Mitsubishi has an infrared tracking feature that we like as it points conditioned air at users, that can add a certain amount of comfort, which often equates to operational efficiency. There may be other brands that have already added that as well.  Along with function and a suitable bottom end operational temperature I would be looking then at warranty and cost. And what is your climate zone? If you are in a more temperate climate then bottom temperature isn't as much a concern.