I rarely cut curves on the bandsaw. When I do, it's usually a long
graceful curve in thick wood that's more than my scrollsaw can handle.
The scrollsaw can cut up to 22" behind the blade. The bandsaw can cut
(at the moment) about 12 feet behind the blade, and it's a lot faster
than the scroll saw.

So what do I use the bandsaw for?

Rough cut-to-length. The TS's original miter gauge is on the bandsaw
all the time (the TS has an incra), I use it to cut small pieces to
length when the TS is rigged up for something else.

Notches. Cutting a notch in the corner of a chunk of wood is fast on
the bandsaw.

Ripping. If I'm going to joint it anyway, it's a LOT easier to rip
hardwoods in the bandsaw than on the table saw - it's like having the
ultimate thin kerf blade ;-)

Kids. My kids can safely use the bandsaw, but not the table saw
(yet).

Resawing. Not just 6" wide hardwoods, but 1-2" wide strips to make
1/4" thick slats. Or taking strips off the edge of a 4/4 board to
make shims or whatnot.

Non-flat wood (firewood), mostly for lathe work.

Plastics, foam, etc - cut quite well on the bandsaw.

Thick wood. Sometimes, it's easier to cut a 6" thick piece of wood on
the bandsaw than do multiple cuts on the table saw - assuming you can
do it at all on the table saw.