Differences between Craft and WordPress This is a super high level question but it would be good to get a couple of summary answers.  What are the main pros and cons of Craft versus WordPress?
I have a lot of experience with WordPress (8+ years), and I like it. I have less experience with Craft (obviously), though I like it more. Here's my 2 (obviously opinionated) cents regarding WordPress vs. Craft:
Benefits of WordPress (vs. Craft)

Free (although a Craft Pro license is super cheap, and you typically need at least 2 or 3 paid plugins to make WordPress usable as a CMS)
Open source (although Craft is built on Yii, which is open source as well, and the full Craft codebase is on GitHub)
Huge community &amp; amount of resources available – although actually sifting through it all and finding quality content can be a chore/difficult – a lot of it is outdated or just bad practice
High quality 3rd party services available for hosting (WPEngine etc), backups/security (VaultPress) and core management (ManageWP) – although if stuff like that is your thing you can use similar services w/ Craft installs; they're just not tailor-made to Craft
Plugin management. Being able to search for, install and update plugins from the Dashboard is great – although Craft will soon have its own built-in &quot;plugin store&quot; and it will be curated, which is a huge plus. Update: Since writing the original answer, Craft 3 has launched and has a built-in Plugin Store inside the Control Panel, which can be used to browse, install, manage and purchase plugins (all commercial plugins have trial versions, and there are loads of free ones too). If clicking buttons in a virtual Store is not your thing, Craft also has first-party support for Composer)
WooCommerce is good (and free) (although Craft Commerce is out and is looking very nice) Update: Craft Commerce 2 beta is now available, and is looking even nicer
Dashboard is easy to use (though I think Craft's CP is on par and IMO makes a better job with keeping things clean and simple)
The built-in media library/uploader/image editing is pretty good (although it still doesn't have folders. Why on earth doesn't it have folders) ** Update: Craft 3 has a simple image editor for cropping, rotating and focus points**
There's a plugin for everything (...and you'll need them. In my experience, Craft installs typically needs fewer – and more to the point; less CMS-critical – plugins.)
There's a hook or filter for everything (although with their inconsistent naming conventions and priority hell you'll quickly build yourself a maze if you're not careful. Craft primarily uses well-documented events to enable plugin authors to &quot;hook&quot; into and affect the app lifecycle, with fairly self-explanatory names)
WordPress has multi-site (although it's pretty half cooked and loaded with gotchas) **Update: Craft 3 also has multi-site, although it's less geared to the use case of running completely separate sites under the same CMS install, and more to the use case of maintaining separate content for different target groups/languages/etc)
WordPress is stable as hell. Not that there aren't bugs, but breaking changes are very rare (there are &quot;deprecated&quot; APIs still in the codebase that are years old). The WP core team is super focused on backwards compatibility, which means important stuff aren't likely to change in a big way anytime soon – however, it also means that much of the codebase is outdated and/or inconsistent. In comparison, Craft is still fairly young and feels much more in flux. This doesn't mean that Craft breaks all the time – it doesn't, bugs are relatively rare and P&amp;T have generally been super quick w/ bug fixing. Compared to WP, there have been bigger changes between major versions, though (mainly for plugin developers, not so much in terms of frontend code/templating or content modelling). Basically P&amp;T/Craft is dedicated to staying modern and lean whilst WordPress is dedicated to not pissing off a gazillion users. These are very different approaches to building and maintaining a CMS, and one may resonate more for you than the other.
– WordPress has a RESTful API built-in. I haven't tried it, so I couldn't say if it's any good. Craft doesn't have a REST API in core, but for the quick'n'easy stuff there's the first party Element API plugin. Beyond that, since Craft 3 came out it's actually quite easy to go totally headless with Craft.

Weaknesses of WordPress (vs. Craft)

No templating engine (some might deem this a good thing. I'm not among them; personally I recommend Timber for using Twig in WordPress themes)
No advanced custom fields – although ACF exist and is a must-have for any WP install. Full disclosure; I actually prefer parts of ACF to Craft's built-in custom fields – for instance its export/import and conditional functionality is stellar. Update: In place of the WYSIWYG of yore, WordPress has this new-fangled thing called &quot;Gutenberg&quot; now, which is kind of like a core modular content system. I haven't tried it, but personally I think it looks like a total trainwreck. Also, both conditionals and import/export is supposedly coming to Craft core in a 3.x update
WordPress is not really a CMS, but a blogging platform – no matter what they tell you. Unless you're building a traditional blog, you'll constantly be fighting the core (yes WordPress has custom post types and taxonomies, but they feel tacked on and are cumbersome to work with, compared to Craft or ExpressionEngine)
The architecture. Most of WP's core and its theme/plugin APIs aren't even OOP, forget MVC. Again I recommend Timber, which in addition to adding Twig support enables you to build themes using an optional, pseudo-MVC pattern.
There's a lot of redundancy. Even as a fairly basic blog platform, there's a ton of built-in functionality in WP that you'll never need for the average site, and that you will want to remove or deactivate. It's like starting with a Pollock painting and applying paint remover until you have something you can draw on, instead of just starting with a blank sheet of paper in the first place
Obtuse APIs (naming conventions are practically nonexistent and the APIs are super inconsistent, which means you need to look up everything)
Security issues (though its actually very easy to secure a vanilla WP install, its still an issue and always will be, as long as WP is the most popular CMS on the planet)
No built-in multilingual support (WPML is decent, but fairly pricy and also big and slow, in my experience)
WordPress is really strict and opinionated about routing, and creating custom routes is needlessly complex (although Timber will help out here, as well)
Hierarchical content and custom ordering is hell (there are plugins but ew)
Confusing relationship between presentation and content. In WordPress, any custom post types or taxonomies is creating w/ PHP code, usually residing in your theme. This creates a confusing relationship between presentation and content modelling which is totally absent in Craft. The big paradox here is that while Craft isn't really designed to be &quot;theme-able&quot;, it still has a much clearer separation between content and presentation than WordPress. (Related WP pro tip: Consider building a custom plugin to add your CPTs and taxonomies, keeping it out of your theme)

Closing notes:
The above is obviously quite opinionated, and I'm clearly partial to Craft.
Obviously, just like with Craft you can basically build anything with WordPress and I find that for the most part, the two systems are fairly interchangeable. There are a few use cases where Craft is obviously the better choice though – e.g. multilingual sites, or sites w/ a lot of hierarchical content. Apart from blogging, I'm having more difficulty coming up with use cases where WordPress is a more obvious choice, which says a lot.
In my opinion, if you're new to both WordPress and Craft, I personally think the experience you'll gain using Craft will be more portable and valuable in the long run, and that you'll experience far fewer gotchas, headaches and WTFs in the process.
Personally, the #1 pro for me w/ Craft vs. WordPress is has been that almost from the get-go (there's a learning cure, sure), I was able to work more effectively w/ Craft than I ever did in WordPress, and I felt more confident about the quality of my work – even with the mentioned 8+ years experience with WordPress. The super consistent codebase/APIs, stellar documentation and Twig templating are important factors here. I also prefer the smaller, super dedicated community around Craft, this SE and the official Slack team being good examples.
PS: I should also note the excellent official support Craft comes with, courtesy of Pixel and Tonic.