The Geometry Engine is a relatively recent addition to the API, having been introduced in version 3.13 and expanded upon with subsequent iterations. However, it's nothing short of a game-changer in respect of the performance of geometry operations.
The Geometry Engine is effectively a client-side implementation of the Geometry Service and, as such, does not need to make any network requests to the server. The result of this is much, much better performance. It includes nearly all the operations that the Geometry Service offers and adds a few more.
Esri has a great sample application that demonstrates the difference in performance between the Geometry Service and Geometry Engine. It uses both methods to generate a 500 mile buffer around 500 cities and records the time taken using each approach. In the following run, the Geometry Service took nearly half a minute to complete the task, but the Geometry Engine managed it in a shade over two seconds:
