If you want/expect stainless, the only way to go is with the Case Sway Back Jack. Otherwise, you're comparing the chestnut bone/CV SBJ to the GEC eureka jacks. The F&F of the Case / Tony Bose collaborations are of a higher quality than their regular knives. Mine has evenly matched bone, no blade wobble, nice walk and talk, no liner gaps, and the springs are flush in the half-stop position. If only I hadn't dropped it and cracked the bone...
I don't own a(n?) Eureka Jack yet, but it's next on my list. Namely, the ivory bone one that Smithhammer keeps torturing me with by posting pictures of. And maybe an ebony one. And a snakewood one. And maybe a second ivory bone one to keep pristine so I can see how the other one ages in comparison. And a buffalo horn one. Anybody got $500 I can borrow indefinitely...?
That said, the SBJ and the EJ are pretty different in size. While the EJ is by no means a large knife, it's definitely larger than the SBJ. The SBJ is smallish...not peanut small, but it's definitely a 3-finger knife, whereas a 3 5/8" knife should be a 4 finger knife unless you have particularly huge hands.
In the end, you'll probably get both. And carry both, if not at the same time. The EJ for most days, the SBJ for when you don't want something as big/heavy in your pockets.