Bandsaws are good for some fancy cuts. Jigsaws are good for when you can put the piece on saw horses or other props. For small pieces, with lots of tight turns, try a scrollsaw . It is bench mounted, but the thin blade lets you turn on a dime without relief cuts required by a bandsaw. So think of what you want to do.
Fret work is a job for scrollsaws only.
The bandsaw is a versatile tool for general stock prep. You can re-saw thin slices for building your own panels. You can use it to cut tendons or curves for rockers or chair backs. For detailed scroll work a jigsaw or scrollsaw is the right tool. I think that both the jigsaw and bandsaw are very useful tools but for really different purposes.