The musical blogoplan is currently under a wave of ten-best- and ten-most-influential-lists, with regard to composers and recordings. I think that best composer lists are pretty much beside the point, as composers are all uneven in the quality of their production and it's the individual piece that counts with the composer, at best, as a kind of brand name, and then more for stylistic than qualitative consistency. These exercises are useful, however, as a modest measure of the sympathies and passions of the moment and can often be useful, too, for clarifying, for example, the distinction between "best" and "most influential" or between an abstract ideal of a work of music and a single representation of the work in recorded form. Thus, Carlos Kleiber's recordings of Beethoven Five and Seven definitely make my best list (and this would be a best list that is far from limited to dead-white-European-male-made classical music) , but I'm not altogether sure that they have been particularly influential, indeed, I suspect that the performances are so good that they are close-to inimitable.
From the lists I've perused at late, it's been most interesting to see how list makers will hedge on the question of influence by including a Wagner or a Schoenberg with a huge caveat about not actually liking the man and/or the music but acknowledging the achievement. Influence is a tough topic and, to be absolutely honest, it forces us to wrestle with some strange notions. For example, weren't Fux (author of Gradus ad Parnassus, the theory textbook of generations of student musicians) and, more locally, Gedalge (designer of the French conservatory "school fugue"), in their bureaucratically pedagogical ways, more directly influential on subsequent generations of musicians than some of the big names? Influence is often a question of on whom, where, and when. Bach, as unavoidably important as he appears now, was an obscure local figure whose complete output was only slowly re-discovered, and even then through the lens of very different performance styles. Or how about that mighty influence that Wagner is supposed to have had? A post-Wagnerian music drama never really established itself, unless we count the Märchenoper of Humperdinck and Siegfried Wagner or the pair of Richard Strauss Einaktors, and Wagner's most radical chromatic tonal practice was not, in practice, that distinctive from late Verdi. Moreover, the developing variations and complex metric ideas of Brahms (i.e. "Brahms the progressive") were arguably the most forward looking technical ideas of their time. No, the lasting influence really comes from that force field of technique in which Wagner, Verdi and Brahms were all working, and eliding any one of those names would come at an unacceptable loss of musical substance. And, of course, once we've eaten up three slots in our top ten like that, it starts to become clear that any meaningful list is not going to be satisfactory with only ten names!