The difference is the so-called "pseudoclassical vs. prototypal inheritance". The suggestion is to use only one type in your code, not mixing the two.
In pseudoclassical inheritance (with "new" operator), imagine that you first define a pseudo-class, and then create objects from that class. For example, define a pseudo-class "Person", and then create "Alice" and "Bob" from "Person".
In prototypal inheritance (using Object.create), you directly create a specific person "Alice", and then create another person "Bob" using "Alice" as a prototype. There is no "class" here; all are objects.
Internally, JavaScript uses "prototypal inheritance"; the "pseudoclassical" way is just some sugar.
See this link for a comparison of the two ways.