Savorino: The primary difference between the original BLR and the '81 BLR is in the receiver shape and, consequently, the clip. The original BLR (1969 - 1980) has a concave-shaped receiver - it is wider at the ends, where it attached to the stocks, than it is in the middle. Consequently the clip is narrower and thus had to be made longer in order to hold an adequate number of shells. The '81 BLR's receiver is straight-sided, which allows a wider and thus shorter clip which is, more or less, flush with the bottom of the receiver.
Owning both, I would say that the '81 BLR is more comfortable to carry because of the flush clip - your hand cradles the receiver as you carry it one-handed, instead of cradling the protruding clip. The other advantage is that the flush clips are readily available, as they are the same as the ones the current BLRs use - the narrow protruding clips for the original BLR are difficult to find and are pricey.
Another difference I can mention is that original BLRs have a front sight hood, while '81 BLRs do not. And my 1980 BLR, of which I am the original owner, has, for some reason, a shorter length of pull than my other 3 BLRs - it is quite obvious standing in the gun rack.
The handling of both models feels the same to me and that is the primary strong point about BLRs, IMO - they just handle great.
pagris
1978 BLR .358
1980 BLR .358
1987 '81 BLR .243
1991 '81 BLR 7mm-08