A lot of guys are going to tell you that .308 is no good with anything less than a 22" barrel. Others will say 18" is the minimum useful barrel length. It depends on which rifle they tend to favor; a lot of the M14 shooters say 22", a lot of the HK91 guys say 18", etc.
On the other hand, the FN SCAR-H that SOCOM is adopting? It comes in three barrel lengths (for the .308 version): 20" heavy barrel (sharpshooter), a 14" standard barrel, and an 11" CQB barrel.
So I don't think it's correct to say that .308 is no good out of a short barrel. Even out of an 11" barrel, it's got more muzzle velocity than 7.62x39 from a 16" barrel, depending on ammo.
Ammo is a factor, though. Standard NATO ball will do about 2,650 from a 16" barrel, give or take. South African chrono'd about 2575 from my 16.25" FAL, but the South African is I think a little underpowered (I had to adjust my gas setting when I switched to it from Portugese).
In the real world, I don't think the velocity difference will make any appreciable difference inside of a couple hundred yards. It will be louder, though, and with no flashhider you can get a bit of a fireball.
I'd get the 16". The 16" Saiga .308 is, in my opinion, an excellent truck/bushwackin'/backwoods gun. Powerful enough for most game animals, lightweight, compact, handy, and tough enough to handle neglect and abuse. They're much more reliable than, for example, a Remington 7400 and cost less to boot.
Recoil is more of a factor of weight than of barrel length. The Saiga carbines are pretty light, about eight pounds maybe, so it's going to get your attention. I don't think it'll be bad, though.
If you're really worried about the muzzle velocity, get the 21", but for plinking and most shooting, the 5" less barrel won't make much difference.
Oh, the REAL nice thing about the Saiga .308s? They can use Wolf steel-cased .308 ammo, which costs about half as much as American Eagle/Winchester White Box/UMC .308 FMJ, with no worries or issues!