I've built many strats, including all the ones pictured here:
www.sparkguitars.com
Some of my necks are quartersawn, some are flatsawn, some are one-piece, others are two piece. It's very hard to describe the difference quartersawn necks make, and it's very hard to even tell a difference, but there is a difference. Quartersawn necks are my favorite necks. I also have an Eric Johnson strat which has a quartersawn neck, by the way. There is just something about them in the way they sustain and snap, and I really like it, but I couldn't tell you exactly what it is. I can barely tell the difference, but whatever it is, I can appreciate it.
It also looks absolutely fantastic. Just check out an Eric Johnson strat or look at my surf green strat and you'll see what I'm talking about. One other thing is that I have to do less fret leveling than flatsawn Maple. However, in my experience with roasted Maple, it also seems very stable, so whatever they cut stays true. All of my quartersawn and roasted necks have required the least fret leveling. It's not like that 100% of the time, but it's more consistent than flatsawn Maple in my experience.
Like I said though, the main difference is cosmetic. I think the advantage of quartersawn is marginal or hardly perceptible, but when you've worked with enough woods, I think you can pick up on some of the nuances even though you may not be able to articulate what it is.