Should use both AppDomain.UnhandledException and Application.DispatcherUnhandledException?

Question

AppDomain.CurrentDomain.UnhandledException in theory catches all exceptions on all threads of the appdomain. I found this to be very unreliable, though.
Application.Current.DispatcherUnhandledException catches all exceptions on the UI thread. This seems to work reliably, and will replace the AppDomain.CurrentDomain.UnhandledException handler on the UI thread (takes priority). Use e.Handled = true to keep the application running.
For catching exceptions on other threads (in the best case, they are handled on their own thread), I found System.Threading.Tasks.Task (only .NET 4.0 and above) to be low-maintenance. Handle exceptions in tasks with the method .ContinueWith(...,TaskContinuationOptions.OnlyOnFaulted). See my answer here for details.