When comparing The Old Reader vs Feedly, the Slant community recommends Feedly for most people. In the question“What are the best news readers?” Feedly is ranked 2nd while The Old Reader is ranked 6th. The most important reason people chose Feedly is:
Feedly has an easy to overview interface. While this interface is clean and simple, it is still full of bright colors. A great feature that adds to the clean feel is "eliminate clutter", which keeps only the text of the desired topic.
Specs
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Pros
Pro Social
People from Facebook or Google can be found on The Old Reader so posts can be shared and discussed.
Pro Very similar to the dismissed Google Reader
Ever since Google Reader has ceased to be an option, The Old Reader has grown in popularity.
Pro Great UI
A clean, easy to use interface.
Pro Easy to use
Intuitive, easy to overview service.
Pro OPML import
Allows for easy migration from any service that supports OPML.
Pro Freemium
Free version has a limit of 100 sites, upgrade to unlimited sites costs $25/year. Being freemium is a nice option for those that would like to try the app out without putting down any money first.
Pro Clean, easy to overview UI
Feedly has an easy to overview interface. While this interface is clean and simple, it is still full of bright colors.
A great feature that adds to the clean feel is "eliminate clutter", which keeps only the text of the desired topic.
Pro Integrates other services for ease of use and sharing
Feedly sign-in is done with Facebook, Twitter, Google, or Microsoft credentials. It offers many ways to share a story from within the application, including social networks, e-mail, etc.
Pro Choice of many different layouts
For each news source, a different layout can be chosen. Choose between showing thumbnails, titles and summaries, titles only, thumbnails with overlaid titles in a grid, or have all content inlined.
Pro Great article recommendations
Search a topic and Feedly will offer resources that are related to that topic.

Pro Supports OPML export/import
With this feature, all subscriptions can be saved.
Pro Seamless Google Reader migration
Feedly have made it especially easy to navigate away from Google Reader.
Pro Similar mobile experience to Google Reader
It supports a list UI similar to Google Reader, among other more graphical layouts.
Pro Browser extensions
Feedly's extension lets users add feeds directly from websites, but also lets users curate pages, save them to Evernote or Facebook, email, or Tweet pages.
Pro Open API
There are multitudes of third party clients available for many platforms.
Pro Boards for organising the content (Paid)
Feedly allows you to create unlimited Boards (folders/sets/collections) and use them to organise your saved content.
Pro IFTTT and Zapier integration (Paid)
Feedly functionality can be extended and workflows automated with IFTTT and Zapier integrations that make it possible to connect the reader with hundreds of popular apps.
Cons

Con Not free/libre
This application is proprietary, and thus cannot be modified, freely distributed, or trusted to be secure. Also, if the developer abandons it again, there will be no way for others to continue to update it.
Con No mobile app
Lacks an official native mobile app, but the mobile version of the site is quite usable and there are apps which support syncing with The Old Reader.
However, users have created many apps for a variety of platforms using The Old Reader API. You can check them out here.

Con Not very customizable
While the sources can be added or removed, the feed cannot be filtered in any other way. Display options are limited as well, leaving the user with the standard view.

Con Long list of paid-only features
Free features are pretty basic. It seems like all the new development goes into paid-only features. Paid features include sharing and saving options, alerts, backup, support or integrations with collaborative tools.

Con No push notifications
Among the most requested features for Feedly is push notification support. The feature was officially requested in 2011 and currently has over 600 votes on Feedly's Uservoice.
Con Log-in is buggy
Logging in can sometimes cause Feedly to struggle. It can become unresponsive and force close.
Con The layout isn't like Google's original or Inoreader's of which is much easier to browse and read quickly
Con Inline adds
Free version puts adds in your feeds
Con No keyword filtering
Feedly has no ability to filter a feed by keyword like a lot of other RSS readers do.

Con No offline support
There is no offline support with the official client.
Con Forces external account to log in
Users are forced to use Twitter, Facebook, Google, or Microsoft login credentials.
Con Steals page views
Feedly has had issues multiple times with hijacking page views from original publishers. See:
Con Organization/sorting features lacking
There is no ability to sort feeds within a folder, and moving feeds between folders is difficult with lots of content.
Con Slow interface
