There are two main technologies in the inkjet industry, piezoelectric printers such as Epson and Canon/HP/Lexmark using bubblejet technology.

An inkjet printer, and this applies to all models, has an ink reservoir or cartridge, that connects to a firing chamber and this is connected to a nozzle - a hole where the ink emerges. The difference between the two technologies lies in the firing chamber.

Piezoelectric crystals are pretty amazing things, when you put an electric charge across them they change shape and they can do this quickly and repeatably. A tiny crystal in the firing chamber twitches and creates a pressure wave that expels a droplet from the nozzle.

A bubblejet printer has a small heater element built inside the firing chamber which heats the ink until it boils a tiny drop, this drop expands explosively and creates the pressure wave that drives the drop from the nozzle.

So the difference between the two methods is not great. However, the consequences of those differences are significant.

A bubblejet head which uses a heater element and boils ink is fundamentally less robust than a piezo crystal operating at room temperature. The heaters can burn out and failure of the nozzle especially if run dry results. More importantly the boiling of ink by the element causes deposits to form on the element (the Japanese refer to it as biscuiting). This will lead to a loss of efficiency over the life of the head. Bubblejet heads tend to be replaced with every ink cartridge change and the head is integrated into the cartridge. Piezo heads are usually fixed for the lifetime of the printer and only the ink is replaced.

This deposit from the boiling process is a practical constraint upon the formulation of the ink and it is pretty crucial that the ink is formulated correctly. Third party inks may be a poor choice.

Piezo heads therefore have a greater formulation tolerance.

Which technology is superior?

Both can do the job at about the same speed and price and, if you can't tell the difference on the paper, ...who cares.