There are a number of reasons why I'm a SNL fan, including an appreciation for sketch comedy in general as well as the massive cultural impact the show has had over the past 35 years. It can be hit or miss, and some seasons are definitely more 'miss' than 'hit', but when the show is running at its peak in terms of cast, writing, and cultural relevance, it's really something.
One thing about the show that fascinates me is that a rerun of a show that plays either on the network or on cable may not necessarily be the same thing that aired from 11:30 pm to 1:00 am ET the night of the original show. When I was building up my collection I noticed that the sketch rundowns of the shows I taped off the Comedy Network didn't quite match the order listed on the episode guide; sketches would often be shuffled around and, on occasion, something would be dropped in favour of either a sketch from another show or material that never made it to a live broadcast. On these shows you could see a disclaimer run at the very beginning:
Most of the reruns I taped were pretty representative of the original show that aired, but when it turned out there was a big omission in the rerun, it could get pretty annoying. There are still a few holes in my collection that I haven't been able to fill just because rerun versions of SNL are so much easier to come by than original airings: by default, any episode aired after the live air date is the rerun version unless none exists (usually the weak and controversial shows would fall into this category).
Older reruns sometimes substituted bits for segments from other shows: a lot of material added to a rerun also appeared in a show without the rerun disclaimer; if a show without a disclaimer turned up in the rerun package, it usually meant the show was not repeated on NBC. Later reruns were a little more unusual in that the content that replaced what was cut didn't seem to be from any other episode. Sometimes it would be a live sketch done in the studio with the same host and cast, sometimes it would be a short film or commercial. One of these bits was actually the Roberto Benigni segment of Jim Jarmusch's "Coffee and Cigarettes".
The reruns from the last 25 years or so (from the point where Lorne Michaels returned to the show after his five-year hiatus) have some more subtle changes. Fans with sharper eyes and ears than mine had mentioned in various places online how the reruns sometimes replaced sketches from the live shows with performances from dress rehearsal. The differences were usually very minor, not really noticeable unless you made a point to look for them or if they made the change to remove something offensive. I did notice, though, the clock on the main stage with no other purpose but to show the time in the studio would sometimes visibly show it was a point earlier during the evening during monologues and musical guest introductions.
From what I guess, the strategy is to make the best possible rerun: if something went better in dress, then that's what they'll use. As well, because a new episode of SNL is live, it's more prone to technical screw-ups, miscues, and awkward "dead seconds"; reruns give a chance to fix some of that. The audio is also remixed a bit for the rerun, which often includes a faint bit of 'sweetening' to the audience response (just a few extra laughs mixed in).
I'd heard of all these things from different sources and noticed a few things here and there when I watched reruns of shows I'd seen when they aired live, but it didn't come together until the night I finally saw a recording of the live broadcast of the first show of 1985-86 hosted by Madonna. This episode is probably the most extensively edited SNL rerun; the most well-known change being that reruns remove the cold opening about Brandon Tartikoff getting urine samples from the cast for drug testing, giving the impression that the show just went straight into the opening montage. Other changes include a second Simple Minds musical performance added to the later part of the show, the replacement of the original Sarah Charlesworth "collage" opening montage with the filmed "limo ride" used from the fifth show of the season on (as well as all bumpers to keep consistent), dead seconds removed, hot mics were fixed, the Weekend Update title card was changed to the one used for the rest of the season, and Don Pardo's line "Two Junkies be located..." in a commercial parody was removed (probably for the same reason the drug testing had to be taken out).
The thing about that live show that really brought everything together for me was the opening seconds of the Weekend Update segment: usually, when the bit starts and Pardo announces "Weekend Update with Dennis Miller", the audience cheers and applauds. On this first show there is no response whatsoever. Miller actually sarcastically quips, "Thank you, Don Pardo, for whipping them up into a frenzy". I didn't remember the audience being dead when I saw the episode before so I checked my recording from Classic SNL, and sure enough, there were cheers and applause (and Miller's comment was left in, dethorned by the editing). It became clear to me how much of a do-over the rerun really is.
What's better? The rerun version seems to be the final product judging by how prevalent these are in SNL packages and how much is done to ensure these are the strongest product. But part of the show's title is that it's live: it's still live in a sense that the sketches were performed in front of a studio audience, but a lot of what's done to the rerun is essentially cheating. Part of the appeal of watching the live broadcast is that anything can happen. Something may not go right. Actors may break character. Somebody might drop a "shit" or "fuck" or tear up a picture of the Pope. You lose the unexpected aspect with a rerun anyway, but the extra editing only takes it further away from being "live".