TextEdit uses the default cocoa text widget. Both TextMate and Safari have reimplemented it. TextMate’s text widget is substantially more sophisticated, and Safari’s is mostly compatible except for a few annoying edge cases (it’s been a few years since I investigated; maybe some have been fixed).

As mentioned in the link's comment thread, ^Y is broken for Webkit. I just tried this in Mail.app and it worked fine.

Amusingly enough, Mail’s compose window uses WebKit for the content area. According to http://webkit.org/b/73888 the issue is specific to the WebKit2 layer that is currently used only by Safari.