This is a very complex subject, with all kinds of answers.
It helps to know WHY you're looking at a new pot for a tree. There are basically two paths--health and art. Ideally you can do both with one pot, however that's a hard thing to do.
Bigger pots (up to a point) offer more room for roots and can GENERALLY improve health. RELATIVELY Smaller pots (up to a point) are used in the "final" stage of development for shows, etc. to make the tree look its best.
Also, FWIW, for their best show trees, Japanese bonsai exhibitors use deeper larger pots for their best trees to grow in day-to-day. Those trees are transferred to smaller, more artistically measured "show" pots a few weeks before an exhibition. The trees are transferred back to the larger pots (and large DOES NOT mean 'huge') afterwards...