Everybody knows about Webform so why would we want another survey system in Drupal? Entityforms takes a very different approach by using an entity and standard fields approach to forms. Entityform submissions are field-able entities.
This has many advantages including being able to use virtually any field module in Drupal. Now you can easily gather geographic information, reference site content and include media references in your surveys and other forms. It also allows for simple integration with popular entity-aware modules such as Views, to handle submission lists and Rules, to handle notifications and form access.
While Webform does have some integration with Views and Rules the process is not as simple as dealing with field-able entities such as Entityform submissions. With Entityforms thanks to the Entity API module, Rules and Views have complete knowledge of the submission information just as they do with the field values attached to other entities such as Nodes and Users.
Also for programmers the process of interacting with Entityforms should be much more familiar than writing custom code that integrates with Webform. As I learned through developing Webform Conditional, programming for Webform is a great way to learn the Form API but your existing knowledge of Drupal programming may not get you as far. Since Entityform Types and Entityform submissions are both entities you can use the standard hooks to interact with them. You can also use great helper classes such as the EntityFieldQuery and Entity Metadata Wrappers to make dealing with these entities much easier.
Multiplier of Effort
A great ecosystem of modules has built up around Webform through the years. This has added great functionality beyond what Webform itself offers(which is a great deal). One problem with this situation is that all of these modules only benefit those who are using Webform. My aim in development of Entityforms is to keep the main module as lean as possible. When there seems a need for added functionality the solution will most likely be an existing or new contributed module. For instance Entityforms currently doesn't have a robust results analysis system. Instead of adding this functionality directly to Entityforms the Field Analytics module was created(thanks to Scott Rigby for his work on this). This way this results analysis will be able to be used on any field-able entity. The need for results in Entityforms then provides benefit beyond Entityforms.
Webform Lives On
Obviously with over 250,000 installs Webform is a useful, reliable, and proven module. The ease of creating new forms in Webform(especially with Form Builder) is currently not matched in Entityforms. In the case that your clients will need to create forms on an going basis Webform seems to be the only game in town(depending on how tech savvy your client is). Also because of the way fields are stored in the database in Drupal, Webform will be able to handle forms with a larger number of questions.
A short video introduction:
Visit Entityforms Project page to download and try it out.