Nearly all OS X apps use Cocoa and standard Cocoa text widgets. Ones which don’t, such as Firefox, usually try to read the standard Cocoa keybindings and respect them. Firefox actually does a relatively good job with this now (within the past 2 years or so; before that, they didn’t).
Both cmd+arrows and ctrl+a/e should work in almost every text box on OS X.
[Unfortunately, applications like browsers override cmd+arrows to switch tabs or navigate through history or something, depending on context... which is IMO a really stupid and obnoxious choice. Browsers typically use cmd+arrows for back/forward except in a text box, where the text bindings take over. I hate it, because it leads to accidentally going back when the user intends the text box movement command.]
The problem in the GP’s particular case lies with gmail’s custom form field though, which is not a regular text widget, not with Firefox.
I might be wrong but from what I remember from two years ago the constant annoyance of switching keybindings between each app was one of the things that prevented me from becoming a fan of OSX and I really tried. (I think the resident fanboy at that site had an explanation about Cocoa and Carbon(?) keybindings but to dumb me it just didn't cut it.)
Nearly all OS X apps use Cocoa and standard Cocoa text widgets. Ones which don’t, such as Firefox, usually try to read the standard Cocoa keybindings and respect them. Firefox actually does a relatively good job with this now (within the past 2 years or so; before that, they didn’t).
Both cmd+arrows and ctrl+a/e should work in almost every text box on OS X.
[Unfortunately, applications like browsers override cmd+arrows to switch tabs or navigate through history or something, depending on context... which is IMO a really stupid and obnoxious choice. Browsers typically use cmd+arrows for back/forward except in a text box, where the text bindings take over. I hate it, because it leads to accidentally going back when the user intends the text box movement command.]
The problem in the GP’s particular case lies with gmail’s custom form field though, which is not a regular text widget, not with Firefox.