I wish GEC's site was a bit more comprehensive with regards to listing patterns and their variants (with accompanying pictures) but it would be a rather exhaustive effort and may or may not be worth the trouble in the end. That said, I did pull a few examples of the different "brown" sawcut Barlows. The pictures are not the greatest (in my opinion) but they might prove to be a valuable reference point for some.
Copperhead Sawcut Bone (If this is the color we could be guaranteed in getting, I'd be more supportive of it. It is far more brown than the yellow and orange examples that are currently being shown)
These two are listed as Antique Yellow Sawcut Bone - note that they differ quite a bit.
Antique Amber - not in the poll above but this first one is an attractive example. I have antique amber on other knives and it's more yellow than this so I suppose it is another dye that is subject to variance. The second picture is certainly more yellow.
Saddle Brown - not in the poll and not a great picture (too much glare)
Dark Chestnut - Honestly, this one doesn't look all that different from the Copperhead examples that have been shown here.
And just for giggles, Muscadine Sawcut. I think this might be considered a red and if I recall correctly, it was a dye that was specifically designed and created for Charlie's last Ancient SFO. Still, it's pretty stellar, even if we may not see it again.