Admittedly, I did not have the time to compare a lot of entries, but the few words I did look up showed a pattern that was hard to dismiss. In all of the cases that I saw, the Oxford dictionary included much more of the history of the word and often went back to the Latin root as well as proposing possible alternate developments of the word. The Chambers dictionary, on the other hand, tended to trace a more linear path and often only went as far back as the Old English or Old French root.
While the Chambers Dictionary of Etymology is a very clear and concise work..., I feel the Oxford Dictionary of Etymology has a slight advantage in precision and depth. Perhaps (as one reviewer has stated) the Chambers has more entries overall, but I feel this has come at the price of a lack of depth of history behind each entry. The Oxford book may have less entries, but each entry contains all the information anyone would ever need.
All in all, I think both books are way ahead of their competitors, but if you want the ultimate in depth, go for the Oxford publication. If you want a good dictionary of etymology at a reasonable price, get the Chambers book.