I have both tools and I seldom use either one. Every tool has a use, and if you have a need to use a specific tool, then it is great to have it. I have used my Dremel tool for things like cutting off small nails on a project I was working on. A cutting wheel works really good for that, but you have to keep the cutting wheel perfectly straight or you will break it every time. In my opinion a Dremel tool is mostly for real small jobs and is not a tool most people would use on a regular basis.
A scroll saw is something I seldom use either, but to a person who creates signs, depending on the signs, a scroll saw may very well be a tool you would use quite a lot. My oldest daughter uses mine to make crafts which she gives away as Christmas presents so most every year she comes over for about a month prior to Christmas and makes stuff to give away. She cuts out little figures and paints them and I must say, they are pretty cute.
She is kind of getting out of it now though, she is working long hours and quite frankly, she doesn't have the "drive" to work all the time and then do this on what little free time she has.
Anyway, my advice is to get the scroll saw, but get a really nice one, don't get a cheap one that you will be sorry for later. If your wife gets it for you as a gift, (I know this will sound rather "tacky" and certainly not "cool" by any means) make sure you give her a "hint" as to which one you want.