How is CiviCRM different in Drupal, Joomla, Backdrop, and WordPress?
Availablity of extensions

The biggest difference is the availability of extensions/add-ons/extra-integrations -- there are more addons for Civi+Drupal, but the differences are shrinking over time.

Civi 1.x didn't originally support its own extension mechanism - the only option was to write a Drupal module. Consequently, Civi-Drupal modules grew first/fastest. The platform now supports plugins on Joomla (Civi v3.3+?) and WordPress (Civi v4.6+) the same way. 

There are a few big-ticket addons that can make a difference for site-builders:


CiviCRM comes with many out-of-the-box forms for event registration, donations, etc. but if you'll be making a lot of customized forms, then the Drupal module webform_civicrm is pretty cool. There are no published solutions which provide as much flexibility on Joomla/WordPress.
Drupal and WordPress have CLI frameworks (drush, wp-cli) which are quite handy for developers and sysadmins. Joomla CLI is still immature.
Drupal Views and Rules are substantial systems which have Civi integrations.
WP BuddyPress is a substantial system which has an upcoming Civi integration.


However, the importance of these differences has diminished since ~v4.2 -- when Civi introduced a flexible, cross-CMS extension system.

Integration features

There are some differences which arise because of distinctive features/norms in each CMS community, e.g.


In WordPress, it's pretty common to embed content in your web-pages using short-codes. Civi has several short-codes in WP.
In Drupal, it's pretty common to embed content in your web-pages using blocks. Civi has several blocks in Drupal.
In Drupal, the core CMS has decent support for "roles" and "permissions", so Civi uses this. In Joomla/WordPress, these are regarded more as "hidden/advanced" functionality, so Civi has to fill in some gaps.


Installation process

The installers are a bit different -- web-based installation is easier in Joomla (because there are fewer forms to fill out), but it's more flexible in Drupal/WP. CLI-based installation is easier in Drupal/WP.

Testing

The core system is the same across all CMSs, but occasionally there are bugs in the CMS integration code. Most of the testing is performed on Drupal/CiviCRM, and it may take a bit longer to identify/resolve bugs in the WordPress and Joomla integrations.