To avoid being accosted, let me be clear and state that what follows is what I like best, subjectively speaking, not what I'm claiming is necessarily THE best merit-wise.
Symphony: The last movement of Beethoven's 9th is so inspiring to me. I get overwhelmed listening to it and thinking of a deaf Beethoven writing it and conducting it. On the other hand, I remember catching my breath involuntarily at first hearing the climax of Mahler's 2nd, 1st mov (Bernstein/NYP). I listen to Berlioz' Symphony Fantastique more often than any other symphony, especially the last two movements: vulgar and raw, something visceral about them I like.
Concerto: I think I have recordings of all the most popular violin concertos (concerti, if you prefer), but it's been too long since I've listened to many of them. Here's a quick "what comes to mind." I think the best 1st movement is Tchaikovsky's or Beethoven's (honorable mention to Brahms and Mendelssohn here). The best 2nd movement is either Mendelssohn's or Saint-Seans' No. 3 or Paul Ben-Haim's. The best 3rd mov. is Brahms' or Mendelssohn's. I may revise this after I go back and re-listen to some I haven't heard in a while (Dvorak, Weniawski, Sibelius, Shostakovich, Prokofiev, Barber).