As someone who develops websites in both ExpressionEngine and WordPress, there is no question I hear more often than Why ExpressionEngine? Why not WordPress (else, insert other open source PHP software here - Joomla, Drupal..)?
Sometimes the answer is, actually WordPress is the better software for this. In these particular cases, you have a blog and pages on the site you need developed. If, however, you dont require a blog and pages, or require another, either additional or alternative feature set, then another software is better than WordPress. Every time.
In the case where another software fits, I have always used, and continue to use, the Ellislab family of products: ExpressionEngine, CodeIgniter, MojoMotor. These are all PHP softwares that run on more or less the same CodeIgniter MVC architecture - my familiarity with this as a framework and these as applications allows me to deliver your project within a predictable time/budget scope, keeping bugs and other unexpected unpleasantries to a minimum. As a client, I would assume you are hiring me for my expertise and professionalism. This is the first way I assure delivery of that to you.
There are other differences in the software, too, besides feature sets. The main difference between the softwares EE (ExpressionEngine, briefly) and WP (similar) is that WP is Open Source and EE is Commercial. Open source softwares are free to download, use, explore, and develop to everyone, no questions asked. WP as a blogging platform has gained tons of popularity based on the needs its able to meet and its availability. Lots of developers, including myself, got started on it. ExpressionEngine, being commercial, has a licensing cost of $300 (or less)- which, while providing salaries for a paid development/support team, also provides a barrier to entry that isnt normally crossed by developers who only want to work with software they can download or use freely. That said, while their numbers are fewer than WP, they are still substancial, (even more) committed, and producing high quality sites at least as much as the bulk of the Open Source communities. The barrier to entry in EE (the licensing cost) keeps a lot of underqualified developers from getting into EE. The folks that are experts in EE (like me) have a lot of practice with it, and prefer it as a platform that is stable, consistent, and ultimately cost saving to the client (you) based on lack of hazard and headache costs, which, believe it or not, we also hate dealing with.
There additional costs of working with EE, paid to developers of add-ons who consider it part of their job to ensure their softwares are meeting the needs of their clients (you, me) and are incorporating features needed by the end user (you, me.) WP developers create add-ons too, yet much fewer are commercial quality. At this point, the end user may face 1) inconsistent code that doesnt get along with the newest version of the parent software or other add-ons used. 2) Lost time (money) looking for a balancing solution to keep all features yet have everything work (this can take days or force compromises.) 3) Malicious code that can compromise site data, if the wrong tool (or theme!) is used. I dont mean to suggest that this happens in every WordPress development situation - it does not. However, paying a relatively small price for an ExpressionEngine add-on (for the price of an hour of your developers time) assures you zero risk of any of the above.
Support in Open Source communities comes at a very high cost (first-party) or is crowd-sourced. Success can vary day-to-day. And if nobody is able to figure out how to help you, you wont get the help you need.
The cost of the EE license covers first-party support for you, the license holder, and me, the developer. All of this can be found here: http://expressionengine.com/forums. Once you sign in (and have a license on your account) youre free to post questions to paid, real-person staff whose job it is to help you get answers. As in both communities, oftentimes your question has been asked before. In the EE forums, you know that the going answer will be the one you need. My personal experience was that I never needed to post any question until a full year after I had begun developing in ExpressionEngine.
Many times, there is overlap as to the features of a website and what softwares can carry it successfully. WordPress is a terrific blogging platform, and it can be stretched to do more than that. Out of respect for the investment being made in me as a service provider, I will carefully consider all of the features you are looking for in your site and recommend software that reflects your websites goals, features, and future growth. Much like a growing child, a website that has not capped at its reach or its potential business impact, is rightly considered to have potential in these areas to grow. And there are platforms that are prohibitive of making certain jumps, and platforms that handle any jump with grace. ExpressionEngine is this platform, as is MojoMotor, its younger page-only sibling, which makes a seamless jump into ExpressionEngine upon being outgrown.