I would say you need both in the shop, they both are needed to do many types of jobs,by the way a good scroll saw will cut 2 x 4 thick stock..
many times I will stack 3/4" thick on top of each other and cut both at the same time..and it can be hardwood.
The snapshots are some scrap 2 x 4 stock,,,the scroll saw can do so much more than a band saw..
and the cut is always so clean you don't need to sand it the norm..plus the blades are cheap unlike the ones for a band saw...and come in many,many types
and can be switch them out quick and easy, unlike many band saws..many will say they can't cut a strait line with a scroll saw , O yes you can with a sharp blade, just like a band saw...
I think the max cut for my scroll saw is 2 1/4" thick
Plus it's the only saw that I know about that will let you back up out of a corner,that's to saw it will cut both ways with a round blade,many times you need to get into a tight place and you don't have the room to turn around with a round blade it's not a big deal, because it can cut both ways...forward and backwards..try that with any band saw..
as you can see they both have a place in the shop..
You need to use your head on this buy,,get a good used pair off Craigs List,many that are selling one off, with have both,it's one of the items in the shop many upgrade all the time so to say the deals are to be had..