Only Barlows I own are Case brand, in some variety of jigged bone. I do think that a nice flat-sided sawcut bone is what my mental picture of a Barlow knife is, if only because that's what the first one I ever saw had on it as a kid (could have been plastic for all I know, but it had that sawcut look).
"Favorite" is a tough concept for me. I like different things different days, and when purchasing knives, if I already have enough of one type of thing, even though it may be a "favorite", I may not want the next one to be just like it.
But since I gotta pick just one, sawcut bone it is.