Mobile-optimized web apps

What are the advantages / disadvantages of a responsive website vs. a mobile website vs. a native app?
- Links:
  - Web-only: A 'responsive' website vs. a separate mobile website (eg 'm.facebook.com').
    - StackExchange - Responsive web design Vs Separate website for Mobile
  - StackExchange - Developing cross platform mobile application
  - StackOverflow - making a mobile application from an existing website
  - Responsive web vs. native apps:
    - Thinkapps.com - Responsive web vs native apps
      - responsive design has two main advantages: time and money.
      - While responsive web is able to self-adapt to any device automatically, adaptive web has pre-set sizes in which it is able to be shown.
      - Drawbacks of responsive web:
        Responsive web needs an Internet connection to work.
        Responsive web usually suffers from poor performance on mobile devices because certain components — such as images and animations — are too slow and heavy.
        Moreover, users will have to wait for the browser to download the entire page and its elements in order to see it. This can lead to a huge consumption of data, battery, and also time.
        if you build an app that is going to be the same for each OS and the web, it will never feel native to users. They likely won’t use your product for long because it just won’t feel natural.
        Lack of Push Notifications, Other Functionality
      - Overall, native apps are a better (but more expensive) option than responsive web.
        [NW: This seems like a clear overstatement.]
      - if your site is just about company information and you would like to invest a small budget, a responsive website might work fine. But, if you are looking for an engaging experience, and your site is transactional, needing more interactions than read and go, I would highly recommend [you] invest in a native application.
    - ModoLabs - My website is responsive, so why do I need a mobile app?
      - I didn't find this extremely persuasive.
      - users prefer the experience of a native mobile app
      - they present navigation, content, and functionality in a way specifically optimized for the measurably different ways in which people actually use their mobile devices
      - Native apps can engage users with push notifications and integration with platform and device capabilities unavailable on display-only websites
      - Users who encounter mobile web experiences that force them to tap, search, copy, and navigate too many times will often give up on their original task. The deep-linking capabilities of a native app keep users focused, allowing them to complete their goal quickly and efficiently.
      - app performance is a significant improvement over a responsive web site, saving end-users time and frustration.
- Misc opinions
  - "I actually am hugely in favour of "web-apps" .. mobile optimzied web... philosophically. In certain cases one or the other is better of course." - John-Paul