* Core functionality is broken between releases. If you ask in the IRC support channel, they will even tell you not to update if things work well! What if I need a new feature?
* Documentation is absurdly horrible or even plain wrong. I have been told several times to refer to the source code to find out how something works.
* If you face any problem, chances are you will never find an answer in Google. You may find some StackOverflow thread if you are lucky, where several clueless people argue about things they do not know and then arrive to a wrong conclusion. (The programming skill levels of Cordova users on those communities are usually very low.)
* Critical functionality (things such as local notifications) is not included. You must rely on 3rd party plugins, that could be well maintained, or could be not maintained at all.
Yes obviously a Cordova app does not look native. It's not native and it will never be. Period.