I'll admit right away I'm a big fan of Drupal and I have never used Kohana, so this post will be one-sided.
In the company I work for they use Drupal or Zend Framework for pretty much all projects (Drupal being in the majority). Many ZF-oriented people dislike Drupal as it's structure is so far from the object oriented ZF-stuff, and Drupal is "just an CMS". As I see it Drupal is more of a Framework than "just" a CMS, and the best part being that it is incredibly flexible: everything is possible.
And yes there is indeed a module for everything. To be more specific:
On the other hand, based on my limited Drupal experience, I doubt building rapid custom >"features" and allowing users to create "groups" and to manage their own roles within >those groups is something Drupal can easily accomplish.
I can only guess what you mean with rapid custom features, but imo it's easy to expand Drupal with your own modules. Most features are available as (free, community contributed) modules, and many advanced looking features can be easily created for example with the "views" and "cck"-modules.
http://drupal.org/project/cck
http://drupal.org/project/views
Creating groups:
"organic_groups" ( http://drupal.org/project/og)
"og_user_roles" ( http://drupal.org/project/og_user_roles )
These modules together are what you need to create groups that have group spefic roles (and roles having specific rights). There are probably other ways than using "og_user_roles", but I'm advertising it because I've made a few patches for it a few years ago. The problem is usually a bit too many options.
If you want to extend group specific options you could code your own module, but most likely you don't need to because there already is a module for it. For example, there are at least 120 modules that integrate somehow with the "organic_groups"-module:
http://drupal.org/taxonomy/term/90?page=19
To simplify, is Drupal capable of true Web Applications; where the application is a >service and provides custom results to each user? Can it provide a dashboard-like >interface for users to change their settings or preferences? Can it aggregate data from >particular users to provide better results/info to others?
In short, yes. There are so many ways to achieve something you described. But probably they would involve at least the excellent "views"-module. I think of views as some kind of ultimate abstraction SQL layer and UI for anyone. And there are over 300 modules that somehow integrate with Views... ( http://drupal.org/taxonomy/term/89?page=55 )
This sounds that Drupal is all about the modules.. and I know some of my collegues even dislike it for that, because you never get to code fun stuff because it's already been done. At least you can look at the module code and learn from that. Or laugh at it, there's lots of badly programmed modules around too.
When you get to coding modules, you'll probably need lots of time to get used to the Drupal API, Forms API, Module hooks, the Theme override system, and the endless options from contrib modules. But it's worth the trouble.
I find this site very usefull to find a module for some specific need. The site shows the same module info as Drupal.org, but also user feedback/ratings, to find the best option:
http://drupalmodules.com/
If it's unclear, my answer would be go with Drupal :)
PS: D7 should be out very soon. Some might wait for it instead of starting with D6. During D5 people would wait a long time before upgrading to D6 because of missing modules. I believe for D7 the most important modules will be available for D7 very fast. Some research at the moment (04.12.2010):
About 190 modules promise to have a Drupal 7 version the day D7 is released:
http://drupal.org/project/modules?solrsort=sort_title%20asc&text=d7cx&display=table
About 130 modules are already available for D7 (most are included in the previous link):
http://drupal.org/project/modules?filters=drupal_core:103&solrsort=sort_title%20asc&text=d7cx&display=table
EDIT: As a newbie I'm only allowed to post one link, so, I removed http:// from the drupal.org-links