The hole saw is for cutting large round holes for things like door handles in wooden doors. They are kind of expensive and require a hefty drill. I use the jig-saw because I have one and I use it for many things. I also have the drill, but it is a small one and has trouble just cutting 2" circle, let alone 3 1/2" circles.
Here is a picture of one:
The largest they had where I found this picture was 2-3/8" and it cost $10 + shipping. Most kits I've seen only go to about 2 1/2".
I did find this place with hole saws up to 6". The 3.5" hole saw was only $9.11, but the arbor that attaches the blade to the saw was another $10.99.
Fine toothed metal cutting jig-saw blades are only $1-2. If you were building lots of cases and needed to cute many holes, then the hole saw would be the best idea. It makes very nice holes.