I expect native app to be written with Objective C (OS X/iOS user here), having very low memory usage, fast startup and offline usage. Also I expect as much integration with the system, as possible, native controls (not that buggy emulation without my favorite emacs-like keybindings) and native behavior.
Probably we miss an important piece of technology: installable web-apps. Website opened in the frameless browser window, identifiable as a different application which could be easily pinned to Launchpad. With all advantages that "separate webview" has, but with some important difference: sandboxing. So I can feel safe when I launch this application, because I don't need to trust all my files, passwords and system to another application. I've seen that kind of technology in the iOS: website bookmark could be pinned as a desktop icon, but it's just a bookmark.