Here's what you should look into: auth: devise gem, crud: Rails defaults + mongoid gem, rest: by default in Rails.
What benefits over CI does RoR have?
Right now, none. You dont know Rails, but you know CI. The time it takes you to learn RoR and its use of "magic" might be better spent writing your application and testing if there is demand for it.
Sure, RoR has a lot of "reusable code", but you don't hknow the framework. And that will just kill your project.
Build your basic app with CI, and then translate it into something else. I wouldnt stray away from PHP if you are proficient with it. You may try other frameworks like Laravel, which is very nice and is more modern that CI. It is also dead-easy to work with. You might also want to check out Python/Flask or even Django, since they are a bit easier to work with than Rails. Im not saying they are better, so put your pitchforks back in the barnyard.
You can extend CodeIgniter's core classes very easily to provide a lot of the same magic you'll find in Rails. There are a lot of ORMs similar to ActiveRecord available, and a great MongoDB library written by Alex Bilbie (https://github.com/alexbilbie/codeigniter-mongodb-library). I've created a popular open source library that enables you to autoload views into layouts like in Rails (https://github.com/jamierumbelow/codeigniter-base-controller).
You can implement RESTful URLs simply and efficiently by customising the routes.php file yourself, or by using a route generation engine such as Pigeon (https://github.com/jamierumbelow/pigeon). If you'd prefer a more "full-stack" REST solution, you could use Phil Sturgeon's heinously popular REST_Controller (https://github.com/philsturgeon/codeigniter-restserver/).
All the above links are drag-and-drop solutions and take moments to download, configure and understand.
You will learn a lot about a whole different kind of writing applications when you learn Rails. But the same is true for Python/Django, the same is true for functional programming languages such as Clojure and the same is true for Objective-C and the iPhone SDK.
CodeIgniter is incredibly flexible and that's probably exactly why you use it. Taking a bit of time to interact with the community and see what gems are out there will let you write much better CI code, and a lot of the time you'll find you don't need or want Rails.
DISCLAIMER: I have written a book about writing better and more Rails-y code with CodeIgniter called The CodeIgniter Handbook (https://efendibooks.com/codeigniter-handbook/vol-1).
I'd say if it's a side project/more wishful success, go with Rails. At the very least, you'll learn something new and improve your skills. If it's something that absolutely needs to work now and is a bit more complex, use your existing CI knowledge for now.
But at some point (perhaps now) I'd just bite the bullet and go with Rails (or Django of course, but either would be a step up).
Personally I've given up on php because they keep having horrible problems with the core (c) code in the stack (not all of which are unique to php, like image processing libraries) -- but I don't think it fair to write off CodeIgniter as an alternative in general.
For anyone looking for a semi-large code-base using CI, I recommend having a look at Bamboo Invoice:
That said I would have been very happy to see more of Expression Engine published under an open licence as well:
My impression is that some of the projects that might have built larger stacks on top of CI just go (or went) with EE rather than write the code themselves.