I don't have Nearly as much experience as many of those here, but here's my take, as a newbie. Maybe it'll be similar to what you'd notice also being a newbie to old steel. When I first got a couple of actual decent quality steel frames(No really high end, but decently respectable. Light version 531 and higher end Miyata) I noticed they were what I would describe as smoother riding and slightly flexier(148lbs) than a new AL race bike. I haven't ridden any carbon other than around a parking lot. The AL is like a harsher suspension sports car that I would ride on a really short ride just to have fun and get a thrill. It's slightly harsh and vibratey, but stiff and slightly faster. The older steel is smooth riding and has more character. Keep in mind though that high end steel is still going to be fast and awesome. I'm not saying a new Ferrari vs. a Cadillac. They're both race bikes. It's just that it's slightly noticeable once you've spent some time on numerous bikes. I personally am not racing competitively, so I'll take the nice steel every time. You notice the difference more the longer you're on the bike. Under 10mi riding fast and just for fun, sure I'd ride an AL bike, but more than that and I'd just rather have nice steel.
Ha! I feel like we could hang out. I drive a BMW E30(90 325i) with H&R, Bilstein sports, lots of other new suspension goodies, and 4.10 diff. Sure, I could have bought a faster "better driving" car for the money I decided to put into this, but the E30 is more Fun. I'd love to add a vintage Porche or a Miata to to my garage someday.