The strange thing is, for me, that while i do believe the music is, in general, quite good, it does just not work for me. As does quite a lot from that era, I must say. Schumann's concerto is among the most popular, along with the Grieg, Tchaikovsky's (or how you wish to spell it) 1st and Beethoven's 5th. But neither the Greig nor the Chaikowsky are among the best, and the Beethoven isn't the best he wrote.
If I woud want to hear a 'Romantic' Piano Concerto, I'd go for the Brahms 1st, even if the Finale is weaker than the rest. Or, to veer out, the Furtwängler...
All best,
gep