Well done for avoidingWe should define what second rate composer means. If anyone not being as great as Bach, Beethoven or Mozart is considered second rate then almost everyone is second rate.
I think the phrase "second rate" is pejorative and loaded with opinion. I much prefer the term second rank -- as of the second rank -- rather like a sergeant to a corporal or a major to a captain. I think it would be much easier to classify composers in that regard without diminishing their accomplishments.
For example I think composers such as Rimsky-Korsakov, Berlioz and Mussorgsky -- all great composers -- probably would not be viewed as highly if you took away their greatest hit. Even counting it they don't have the accomplishments of composers of the first rank -- Beethoven, Mozart, Bach, Schubert, Mendelssohn, others -- who wrote masterpieces in almost all genre.
A third rank, then, might be still great composers without a defining piece of music. This might include the likes of Copland, Telemann and Henry Purcell -- all great composers that didn't write that one (or more) great hit(s) like Berlioz's Symphonie Fantastique and Rimsky's Scheherazade.
Then a fourth rank might be composers that don't have the body of work of people like those three -- multiple compositions in the standard repertory that have been played and recorded again and again over time.
Using the original post as the "General" category we could say:
General (first): Mozart, Beethoven, J.S. Bach
Colonel (second): Brahms, Haydn, Tchaikovsky, Handel, Schubert, Schuman, Wagner, Verdi
Major (third): R. Strauss, Dvorak. Prokofiev, Shostakovich, Sibelius, Stravinsky, Mendelssohn
Captain (fourth): Ravel, Britten, Chopin, Debussy, Liszt, Vivaldi, Vaughan Williams, Rachmaninoff, Elgar, Mahler
Lieutenant (fifth): Puccini, Rossini, Saint Saens, Berlioz, Bartok, Walton, Strauss family, Mussorgsky, Monteverdi, Faure, Donizetti, Hindemith, Messiahn
Sergeant (sixth): Weber, Grieg, Copland, Telemann, Purchell, Poulenc, Bruckner, Sullivan, Rimsky-Korsakov, Schoenberg, Janacek, Franck and Martinu
This is everyone that scored 15 points of more in my survey. Thus it makes Dvorak a composer of the third rank.
See how silly that sounds? That is the difficulty in ranking greatness in any way.