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The R2 2-disc release from last year essentially has the same transfer (apparently split over 2 discs to accommodate DTS which the Criterion doesn't have) and extras taken from the Criterion release.
Generally, Criterions are more expensive since the company tend to make more of an effort by getting a new transfer and obtaining high quality commentary and extras. I've found they've been worth the extra money - eg the recent release of Videodrome was stunning, in terms of the film, the extras and the packaging.
1) Do The Right Thing. Amazing transfer, they really went to town on this with the overall quality very, very good. Extras (disc 2) are the usual extremely high standard you come to expect from the masters.
2) Traffic - again, a better picture, as good as you'll probably get considering the type of film. Extras (Disc 2) again are outstanding with a whopping 25 deleted scenes with commentary being the highlight.
Generally speaking if you love a particular film and it's available on Criterion you should snap it up as they are filled with the extras you want, only available for a set period, and inevitably carry enhanced picture quality. For a full list see