Most scroll saws shouldn't have any trouble cutting one thickness of 18mm ply (a little less than 3/4" by my rough estimate). Two thicknesses would give it more trouble, though a high end scroll saw will still work.
I can see a few advantages to useing the scroll saw over a jig saw (Here in the states we call them saber saws, so forgive me if I slip from one term to another).
1. The scroll saw will produce a smoother cut. Most saber saws I've used really butcher the wood around the cut, unless you are using a fine blade, which just takes longer. Scroll saws, especially if they are equipped with a reverse-tooth blade, will require almost no sanding. I sand up to 220-grit before cutting, and then just go over the piece with 300-grit before applying a finish after cutting. The only real sanding required is if you get off your lines or flub a curve.
2. The scroll saw with a little practice, will give you more control on delicate cuts and curves. It isn't good for a long, straight cut, but smooth curves will work with a bit of practice.
3. The scroll saw requires smaller blade-entry-holes. I'm not sure if that is a prime consideration, but it is still an advantage to the scroll saw.
4. A scroll saw with a spriral blade will cut in any direction.
Now if you are cutting something large, the scroll saw is limited by the size of the table and that throat. That is definately something to keep in mind
Best Regards,
Bob Duncan
Technical Editor
Scroll Saw Woodworking & Crafts