I have been using WordPress and ProcessWire as a designer and frontend developer for a while now. Everything I mention from here on is from that perspective and this is an important distinction as both systems cater towards different audiences. Jeff, I get that you wouldn't choose ProcessWire, that's a very personal choice and probably the right one for you as long you don't want to learn frontend development.

It's very easy to get caught up being in one camp or the other and the biggest determining factor in which you are in depends on what your level of experience is and in which area you focus. The fact is that the two systems (WordPress and ProcessWire) are very different with philosophies that are very separate from one another.

WordPress is engineered to help people publish content, as quickly as possible and leans heavily towards blogging functionality. WordPress is probably the best in the industry at this. Whereas ProcessWire has been created to help designers with (frontend development experience) and developers to create very bespoke websites, quickly and in a streamlined way that ensures you only create what is needed for the job in hand.

If you don't have any interest in learning frontend development practices, you will have a very difficult and unenjoyable journey with ProcessWire. In that case, currently, WordPress is hands down the best choice for you of the two. However, on the other hand if you are a designer with technical frontend development capabilities you will probably find ProcessWire superior in most ways and can probably create more lean and efficient websites than with WordPress.

The closest comparison between the two I could draw would be to say that (out of the box) ProcessWire is similar to starting out in WordPress with only pages, Pods and Advanced Custom Fields built into its core. You loose the posts, taxonomies and comments installed out of the box (they can be fairly quickly built with the Pods and ACF interface) but you gain amazing flexibility in how you want to approach the build of your site.

Because WordPress is so popular, I am finding that around 80% of my work is done within WordPress at the moment. As a designer / frontend developer I seem to be attracting a lot of clients who actually ask for WordPress. I love WordPress as I find it easy to work with and the admin interface is stunning - aiding its immediacy for my clients. It's very simple and quick for people to publish with the platform. However, there are a lot of things that bug me about it and as a developer I spend a lot of time turning things off within it, whether that is the WP Generator meta tag, comments or even posts etc.

If it were my choice I personally would go with ProcessWire nearly every time, mainly because as others have pointed out here, that you can control the markup and functionality entirely. ProcessWire doesn't make assumptions on how you want your markup displayed and the admin interface can be more easily tailored towards the client needs. The fact that I can easily create repeating field groups in the admin area and use a very simple jQuery style api to display the results, much more quickly than I can in WordPress caters towards those with more bespoke requirements perfectly. You just loose those turnkey capabilities in ProcessWire and for some jobs you will have to charge more.