Some comments to the Times obituary point out that Allan Kozinn neglected to say much about Abbado's health problems and how they affected – deepened – his conducting. It was very much a topic of discussion during the past ten years.
Also that the Bernard Holland review Kozinn cited was actually a negative one. Holland said, "Beethoven’s rough surfaces are sanded and polished to a shine. The sweep of a melodic line takes precedence over the absolute clarity of inner voices" – which is sometimes not a good thing.
On the other hand, David Nice (part of dirac's link above) says –
A recording producer defined his special gift as a sense of "absolute pulse" – more precisely, an unerring sense of the right and natural tempo relations in a piece that could give shape and meaning even to the most seemingly amorphous of works, and within that a supple life to the individual musical phrases that no contemporary has equalled.
& Andrew Clark sums it up best at the Financial Times –
The great paradox about Claudo Abbado who has died at his home in Bologna at the age of 80, was how someone so uncommunicative in rehearsal and in private could open up such powerful lines of communication in performance; how a conductor who was the opposite of a domineering careerist could reach the pinnacle of a profession notorious for its big egos...
He will be remembered above all for his Mahler, which was more tender, linear and melodic than most: like his Wozzeck it was subtle and beautiful rather than jaggedly neurotic. He was a superb interpreter of Schubert, Rossini and the second Daphnis suite, to which he brought sweeping power. As an opera conductor he returned again and again to pieces that were difficult to pull off – Boris, Pelléas, Fierrabras, Simon Boccanegra, Don Carlos. His Mozart was a little pedestrian, his Brahms serious and faithful, while in Beethoven he was an old-school conductor who, unusually, was willing to learn from modern “period” style.