There was a fairly extensive discussion of the respective merits (and indeed necessity — or not!) of band and scroll saws in the early parts of the Tiddler by Vic Smeed thread (**LINK**); my own contribution to that discussion was quite similar to what David Marks 1 just said, namely the following (I quote):
"I'd say that that depends on what one's priorities are.
A bandsaw has the disadvantage that it simply cannot be used to do internal cuts like cutting out the interior of a closed frame. Because the blade is a continous loop, you just cannot get it in there without at some place cutting through the periphery.
With a scroll saw this is not a problem: one just slacks off the blade tension, unhooks the blade at one end, threads it through an initial drilled or otherwise created hole, hooks it back up and retensions the blade.
On the other hand I have found it neigh on impossible to do a perfectly straight cut with my table top scroll saw: even with a guide for the workpiece, the blade is too flexible and it just won't cut dead straight. On that point the bandsaw is many times better, and with a bit of normal care makes it easy enough to do long, straight cuts.
As for curves, I find the bandsaw better for getting a nice, smooth and gradual curvature, whereas the scroll saw, with its much thinner blade, can make tighter turns.
When looking at these kinds of saw don't forget to take into account that they both suffer to some extent from throat issues. Not of the coughing kind, but they both have a limit as to which depth of workpiece will pass between the blade and the back pillar.
These two types of saw are thus not, I think, so much alternatives for each other as complimentary. What the one does very well the other does less well so, and vice versa.
Having both, I'd say that if I could have only one of them I would plump for the bandsaw, which I use much more than my scroll saw."
/Mattias