Barbirolli's Sibelius was the first cycle by a single conductor/orchestra that I bought, because it was praised in the classical press. At the time, I thought it was good, but lacking in tension. I've since acquired several sets, as well as many singles, and have not listened to the Barbirolli in quite some time. I'm not fixated on tempo. For me, the secret of Sibelius is tension, which can be achieved at faster or slower tempi. Without it, the music (to me) is just sort of "there" -- not going anywhere, even boring. With it, the music is sublime. So, I like Vanska/Lahti, Segerstam/Helsinki, and (urp, dare I admit it) even much of the Maazel/Vienna cycle. I also like listening to Bernstein's cycle at times, but need to be in the right mood for that.
Actually, I've been digging around in corners of my brain to think of recordings by Barbirroli that I do like. Because I don't really much like his Mahler or his Bruckner. I got rid of all of my Barbirolli/Bruckner and have only his M5 and M9 now. I'm not sure why I kept those. I haven't listened to them in quite some time.
The classic Barbirolli, of course, is the recording(s) he made with Jacqueline du Pre of the Elgar Cello Concerto. Both recordings. The studio recording with LSO, is the common first choice. But I also like even more the live recording with the BBCSO. He also recorded the Brahms Piano Concertos with Barenboim, which I've considered better than most, although not first choices against some very stuff competition.