It is highly variable.
First of all, "Swamp Ash" is not a species of tree, or even a specifically and/or legally defined type of lumber. It's just a marketing term used these days to try and sell guitars, and nothing else. That's it; it has no real meaning beyond that. Originally, it was called swamp ash only to roughly label what region it came from. Those areas have now been pretty much completely deforested, and true "swamp ash" (i.e. ash that just happened to grow in a swamp) is basically impossible to find as lumber. Nowadays, when a guitar maker calls something "swamp ash," it is usually just the pieces of ash that happens to not weight a ton...though there is no official set of specifications for what can legally be called swamp ash and what cannot. They just know that people want "swamp ash," so they call it that. In other words, "swamp ash" is a pretty much meaningless term these days. All it basically means is "ash," and, TMK, no other industry uses the term "swamp ash" today.
That said, no matter what it is, it does sound different than alder. It tends to be a more middy and less bottom heavy wood.
...and THAT said, every chunk of wood is very different. You will have significant variation within species, such that the ranges of variation will overlap. For instance, I've had "swamp ash" guitars that were very dark, and alder guitars that were brighter than normal. If I'd had to do a blind test, I would have assumed that each wood was the other, based on common generalizations about those woods.
In other words, if you're just building one guitar here or there, you never know what you're gonna get by choosing a certain type of wood. In order to establish tonal predictability in the construction of a guitar, you're gonna need to build tons of them, in order to allow a natural average to make itself clear.