Lutejones,
Thanks for your post. I find it incredibly interesting to think about American traditions as viewed through your eyes from Spain! One of the things that I love most about traditional designs is their ties to the cultures that produced the design, especially with regards to the different work traditions that produced the need for the knife. That will factor into what follows...
One way I sort out folding knives is by size. There are large utility knives like the Opinel #8 & #9, Buck 110/112 folding hunters and the German butcher's knife (we call them sodbusters). I would put the large stockman knives into this category. In this size range, I think the suitability for "pocket" carry needs to be understood in terms of traditional work clothing. Knives of this sort fit into vest/jacket pockets, the pants pockets of baggy and tough work pants in situations where the "imprint" of the knife doesn't matter and into pockets specially made to carry tools. Most days, I wear baggy carpenter's jeans and my EDC rotation is between a French Opinel #9 or a Buck folding hunter (112 or 500). The Bucks in particular are bigger and heavier than your large stockman but they work just fine for me (and my clothing choices) for pocket carry. The thing will all of these big knives though is a tie to heavy rugged use that favors a bigger knife. How it gets carried follows after that and the comparison is not to other smaller folders but to small fixed blades. Large folders can be put into (large) pockets and fixed blades can't.
In my mind, the next steps down include "medium" and "small" knives. I would put your Barlow in the medium size range. But as others have noted, I think of the Barlow as more of an English design that persisted in the US. That alone is an interesting point of US culture. Most of our culture is formed by our history of immigration (and to be fair, destruction of native culture). The Barlow is like the German butcher's knife. They're European designs that took hold here. I guess I would have to toss in the American Camper/Boy Scout pattern in with this bunch. Very closely related to the Swiss Army knife. Other American knives in this category are more reflective the emerging American culture. The equal end cattle knife and medium sized stockmen would be in this category. I associate them with the cowboys of the American west. There are also the canoe and medium sized trappers, which I associate with the hunters and trappers of the American north woods.
I associate smaller knives with the rise of the business man. Often they're referred to as "gentlemens' knives" and I associate them with more genteel task like opening letters and with more citified dress slacks where a large knife would be too visible. Whittlers, peanuts, congress and senator's knives are often found in this class.
No right or wrong here. Really depends on what strikes your fancy and suits your carrying needs (related to your dress style).
You mentioned wanting a thin profiled blade so I'll toss out one of my favorite "American" designs in the medium sized class for consideration and that's the Camper/Boy Scout style knife. They typically a very flat ground spear point blade. If you like a flat spear point but want other cutting blades, you might look for an equal end cattle knife. Similar to the stockman in terms of having 3 blades but can be found with a spear point instead of the clip blade.
Here's a 70s vintage Camper. I associate this design with the "camping" and scouting ideal of the early 1900s. Very much the romantic movement of retreat to the outdoors for health and well being.
camper-leaves by
Pinnah, on Flickr