I don't know all the in and outs of the differences, but...
The model was meant to be a faithful reproduction of the original SGs when they first appeared. But a standard model, not a custom shop guitar. They were discontinued when the wood raids and stuff happened. The SG fanatics have been going "when is the 61 RI going back into production?" but have been fearing that Gibson were only going to do it as a custom shop thing rather than one of the standard models.
Back in November or so, some folks in the US were going "omigod, look 61 RIs in this shop, even though they're not on the Gibson lists". They disappeared, reappeared, folks were arguing as to what they actually were. Apparently in early Jan some appeared in the UK. Rumour has that it that the guitar is now "back in production officially" even though it's not mentioned as part of the 2016 range or marketed by Gibson so far.
Anyways, the neck is "slim 60s taper" - it's VERY slim compared to my Faded SG and Les Paul, I think it's even thinner than my Explorer. But it feels "wide" - it's very fast.
The headstock is loads larger than the Les Paul and later SGs (so danger of severe neck dive if you don't put a decent strap on).
It has the small pickguard as opposed to the "batwing" that has pickups mounted on it (and the bridge mounted through it).
It comes with 57 Classics as stock pickups (although I'll probably replace those).
The "tune-o-matic" bridge is the original ABR-1 design rather than the Nashville - although this might prove to be a problem for me when I put heavier strings on, the ABR has less travel for intonation adjustment. But the real cork-sniffers reckon the ABR gives better tone or something (screws straight into the body, rather than into mounting bushes). Who knows? It sounds great and is all in tune at the moment...
The body shape is slightly different than later/modern SGs. I'd always heard this, but now I can see exactly what they mean with it side-by-side with my Faded. The bevels on the edge are much more pronounced (the edge of the guitar is loads thinner) but "softer" in shape. It makes the guitar look bigger from the front but much more feminine from anything but straight on.
There's probably some other stuff - but I'm not a real expert SG-sniffer! I was drawn to them originally because Vince Melouny played one in The Bee Gees in the 60s. Also, sound-wise, they're kinda closer to what a strat does, so they've been the Gibsons that a strat-player like me always wonders about... Then, of course, there's Angus (I'm trying REAL hard to stop playing Angus stuff... but it just kinda sneaks out!)