I enjoy both works. The solemn darkness of the first movement of the Schumann is balanced by some beautiful moments (the second theme, anyone?). I do think that the third movement does not flow as well as the first, although one can say this of other violin concerti too (as in Tchaikovsky's concerto - love the work, but not sure about the lethargy of the slow sections in the finale). As I recently mentioned in another thread, I think that Mendelssohn's E minor concerto is one of the most perfect works structurally and expressively. It also works nicely on the fingers.
Mendelssohn's D minor, though somewhat immature, is also worth a listen. Not bad, considering the guy was 13.