The extremely flexible API of ProcessWire (no template engine here, just pure PHP in a JQuery inpsired API [1] ) lets you expose parts or whole of your website structure as JSON REST services (or XML, or plain text, or RSS, or what want you).
As a bonus, the it also makes writing simple pure-php "templates" (yea, its not really templates, but) super easy. You basically just drop in your HTML/CSS/JS stuff, and add a few pw api lines here and there, and you're done.
In my experience after 8 years of Drupal experience, and 1 year of ProcessWire experience, is that PW is what Drupal should have been from the start: Elegant, Lightweight, Fast, and Flexible. I'm sold!
[1.a] http://cheatsheet.processwire.com
[1.b] https://processwire.com/api