AFAIK, there are no differences in the movie itself, only in the extras. The SE has some additional extras, including an alternative ending, from what I hear.
I have the older director's cut as you might have guessed. It is anamorphic and DD5.1. I hope you are not considering buying that one though, as the SE is a good price and should be the only one you purchase now. (If I did not own True Romance at all, I would buy the SE now without hesitation).
I have the older one and was wondering if i should sell that one and buy the new one.
The cover of mine sais it´s letterboxed.. nothing about anamorphic. It is dolby digital.. but sais nothing about 5.1. And I see nothing about it being digitally remastered. BUTif it is all of that.. anamorphic , 5.1 and digitally remastered... then I see no reason to change. Am only interrested in picture and sound quality.