I have only tried the seated version once when I trained at a buddy’s gym, as mine only has the lying version. I liked the seated version much better, and could move the whole weight stack, whereas with the other version I can lift much less weight.
If I have to speculate on the reason why that is, I think it has to do with the length-force production correlation there is when it comes to muscle, i.e. a muscle can produce more force when it’s slightly elongated and much less when it’s close to full shortening.
When you’re seated, your hips are in a flexed position, hence your hamstrings (the part that crosses the hip that is) are pre-stretched, and that might the reason why you can produce more force, as opposed to when you’re lying down and your hams are partly shortened, already.
As a side note, one reason why I don’t particularly like the lying leg curl is that it’s very hard, at least for me, to keep the lower back out of the movement. I always tend to compensate a little when I’m fatigued, no matter how much I try to brace my abs to counteract that.
Bottom line is, if I had a seated leg curl at my gym, I’d totally use that.