You may have noticed that some espresso machines list vibratory pumps, and some list rotary pumps. Prime examples of this are the rotary and vibratory versions of Rocket Espresso's Mozzafiato and Giotto machines. In the case of these machines there's the "Type V" or vibratory models, and the "Type R" or rotary models. Outside of the two different pump types there's not much that separate these machines. So why the difference in price? To understand, let's go over the two types of pumps more generally.
Vibratory
A vibratory pump uses a pulsating piston to draw in water from a tank and then pump through the boiler. These pumps work well for reservoir fed machines that are a bit lower volume. They're affordable, less susceptible to limescale buildup, and quite simple. Their affordable cost also keeps them from being too expensive to replace should the pump fail. Finally, these pumps are small enough to fit in more compact machines, making them ideal for home use. The biggest disadvantage of these styles of pumps is you can't use them with a direct water line. This is because the pump can't handle the incoming pressure from a plumbed in water line. They can also be quite noisy compared to rotary pumps.
Rotary
Rotary style pumps usually come in two parts, with a motor and a rotor that pushes the water through the water system. These pumps are more robust than their rotary cousins, putting up with more volume and the increased load of a plumbed in water line. They can also lead to more even pressure when brewing, as there's an immediate ramp instead of a slight lag like you might get from a vibratory pump. These reasons are ultimately why you tend to see rotary pumps in commercial machines. These commercial machines are also large enough to accommodate the larger, heavier assembly of a rotary pump. In home machines like the aforementioned Mozzafiato and Giotto Type Rs, you're getting a pump similar to what Rocket Espresso uses in their commercial models but a little bit smaller. It will still be able to handle the plumbed water line and higher volume.
Which is right for you?
So the question becomes, which of these pump styles is right for you? Does it make sense to pay extra for a rotary pump? The biggest question for a home user is the plumbing in question. If you don't intend to plump the machine into a water line, then a vibratory pump really is all you need. If you do want the option of plumbing in then it's worth the upgrade to that rotary pump machine! Regardless, if you end up going with a Rocket Espresso machine, you can be sure you'll be pulling shot after shot of great espresso.