Hi Cleav, that is a lovely pocket watch. I'm sure you will enjoy using it. I'm afraid I don't have much background with regard to pocket watches. Hopefully, you will be able to find some information about your pocket watch via the net.
I they are a bit more complicated to make, and at least many years ago, they were tougher to make water resistant, as you had sort of irregular shapes and sharp edges involved with squares and rectangles, which don't can hinder the longevity of gaskets if pinched. In addition, you often do not have the same economy of scales with square, rectangular, or asymmetric cased watches. You are often limited by the shape of the watch, in terms of the movement. Round movements will fit in any case shape, but if you use a square, rectangular, or asymmetric case, you have to use a much smaller sized movement to avoid the constraints caused by corners...in this case putting a round peg in a square hole. Still cheaper to go that route than to make a square or rectangular movement as many companies focus on round watches, so its not cost effective to make square or rectangular movements for what might be a tiny bit of their annual production. The handful of companies that go through the trouble of making square/rectangular movements are AL&S, JLC, and Piaget. On occasion other companies do, but most times even Patek and AP just use smaller sized round movements and put them in rectangular pieces (Yes I know PP's 10 day Tourbillon was a rectangular movement, but that seems to be less common for them). I love non-round dress watches, as it really feels like dressing up going from one of my steel round sport watches to a RG square, rectangular, or asymmetric cased watch. I think also, most men find the fancier case shapes a bit too dressy for them...and not sporty enough. It can seem like a big transition for some to go from a round watch to a non-round watch.
Below is one of my favorite pieces from Cartier, specifically because it used a rectangular movement rather than a more cost constrained smaller round one.
Frills, yes I had noticed that in that image involving the stick figure with the AP...his crown appears to be a Rolex crown. I thought it was amusing.