Composers span the spectrum of genius, great, functional, appealing and so many more. Mozart wrote music in his head and then merely had to write them down. Beethoven composed while deaf. Bach consolidated one of the most important schools of harmony and on top of that, was a masterful organist and organ inspector. Chopin was the master of emotion and chromatics. Liszt was a showman that kept people riveted. Tchaikovsky composed amazingly for the ballet in a way few have rivaled and he had a brilliance for catchy melodies. Haydn could churn out music on command (over 100 symphonies?!) Brahms was king of melodrama (not that its a bad thing in music). We have Schoenberg creating a whole new school of tonality...or lack thereof.
As you can see, its hard to choose. It's very subjective and even objectively, you'd have to pick a category by which to judge.