When comparing ProcessWire vs Strapi, the Slant community recommends Strapi for most people. In the question“What are the best open source headless CMS's?” Strapi is ranked 1st while ProcessWire is ranked 4th. The most important reason people chose Strapi is:
Strapi comes with blueprints that let you create, read, update and delete your data. You also can paginate, sort and filter your results in a matter of seconds with simple but yet specific parameters.
Specs
Ranked in these QuestionsQuestion Ranking
Pros

Pro Nice and helpful growing community
You will always find one to respond politely in the forums. Sometimes even the creator Ryan Cramer himself.
Pro Custom Fields on steroids
ProcessWire is heavily based on custom fields. All objects (Pages) inside ProcessWire are based on extensible templates comprised of fields that can be easily defined. Many useful fields come prebuilt and they can be extended with modules.
Pro Easy to learn
Processwire is extremely easy to learn. Consider this:
echo $pages->get('title=Hello World')->title; // "Hello World"
echo $pages->get('title=Hello World')->parent->title; // "Home"
echo $pages->find('Template=Category')->count; // 126
echo $pages->find('Template=Category')->each('title'); // ['Audio', 'Video' …]
Selectors are so powerful but yet so easy.
Check out the cheatsheet.
Pro Powerful and easy API
The API is jQuery like;
// find some pages:
$pages->find('template=skyscraper, architect=john, sort=title')->limit(4);
// mutate
$pages->get('title=Hello You')->set('title', 'HelloWorld')->save();
$pages->get('title=Old')->trash(); // trash page
// check user…
$user->isLogedin();
echo $user->name; // guest
$session->login($name, $pass);
$session->logout();
// redirect
$session->redirect($url);
Pro Powerful selector engine
The way you fetch, access and manipulate objects (Pages) in ProcessWire is extremely powerful and easy. You can receive any page and its custom fields, filter, travers, add…
Pro Template Engine Agnostic
By default, ProcessWire comes with 0 assumption on how you handle the output. You have 100% freedom on how you want to develop the frontend. Want to plain output stuff, go ahead. Want to use any number of Templating Engine, do it. Just use as Headless-CMS, okay!

Pro Extensible
Either using the modules already available or writing your own module, using the jQuery-like API.

Pro Open source
Source available on GitHub.
Pro Auto-generate REST APIs
Strapi comes with blueprints that let you create, read, update and delete your data. You also can paginate, sort and filter your results in a matter of seconds with simple but yet specific parameters.
Pro Users, groups and permissions
Manage user settings, login, registration, groups and permissions on the fly. Strapi delivers all those essential features out-of-the-box.
Pro Out-of-the-box administration panel
Easy way to manage your application. This panel allows you to add/edit/delete entries for your APIs, manage your users, groups and permissions. In the future, it will be such as WordPress-like administration panel dedicated to your application.
Cons
