not full speed of your PC,
not enough hotkeys,
no giant lists without pagination,
no confidence that new/old version of browser will not break something,
obstructions of using 100% of display without pressing F11
and, of course, no ability to work without Internets with no afraid to wipe off "offline first" part of application if pressing something like F5 or Ctrl-W.
A web application pros: no troubles with exotic architectures, no piracy (if we are talking about proprietary things), easy networking.