As the bears eat, you said it looks like the two editors have different opinions about how wide the tab is. By default, the tab character ( \t) is 8 spaces in emacs. Maybe TextMate shows the tab as 4 spaces in your configuration?
You can set the tab width in emacs (up to 4 spaces in this case) by adding the following to your .emacs:
(setq-default tab-width 4)
I don't know anything about setting up TextMate.
Alternatively, you can configure emacs to use spaces rather than tabs for indentation:
(setq-default indent-tabs-mode nil)
Again, I do not know how you do this with TextMate.
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