Leonard Bernstein recorded the Symphonie fantastique three times over a relatively short period: 1963, 1968 and 1976. The first two, with the New York Philharmonic, were for Columbia Records (CBS/Sony), the third try was with l'Orchestre national de France for EMI. He left multiple recordings of other works, but none over such a short time-span. The easiest way to tell them apart is by checking the timing for the 3rd movement,"Scene aux champs" : 1963 = 17:14 1968 = 15:09 1976 = 16:32 All three recordings have been issued on CD. The EMI recording is easy to find. Unfortunately, CBS has confused the situation with the two New York recordings.
Personally, I prefer the 1968 version, even though it is only available on the early "Great Performances" CD transfer with no fillers: Hector Berlioz: Symphonie Fantastique (CBS Great Performances). The 1963 version sounds the same on the "Bernstein Century" as it did on the "Royal Edition". The former is coupled with 2 overtures and a march, the latter with a 15 minute talk, "Berlioz Takes a Trip," (recorded in 1968 with musical examples taken from the 1968 version).
Which brings me to my all-time favorite performance of this symphony by Bernstein. It's from 1969, but it's not on CD. It's on DVD, part of a 10 DVD set: Leonard Bernstein - Young People's Concerts / New York Philharmonic. It's not as expensive as it sounds - about $90 (new) on Amazon. The May 25, 1969 broadcast is "Berlioz Takes a Trip," an hour-long version of the 15 minute talk on the "Bernstein Century" CD. It does not include a full performance of the symphony, except for the last movement, but all the juicy parts are there, and Lenny was always more fun to watch and listen to than to just listen to.