Chuck, for anyone coming to high speed service from dial-up, they'll see a big difference. As RecoilBob says, it's the size of the pipe and the pressure that determines how fast you receive data. But the other side of the equation is how much pressure and volume the server is sending to you.
That said, I had 1.5 mbs DSL service and when it was upgraded to 3 mbs speed (gratis), I thought I'd see a big bifference. Didn't happen, made no difference. I can go to a speed test site and verify that I get about 3 mbs download, but it rarely happens in real life. Many files that I download open a window that shows transfer rate. The highest I've observed was about 1.5 mps. Most are around 500k (0.5 mbs).
I think it's because of several issues. Some sites don't have the capacity to send as data fast as you can receive it. And some sites limit the way they apportion their upload bandwidth to make sure that one user doesn't get it all and others are left without. A good example might be your local paper or TV weather site. They may have 50 mbs of upload bandwidth, but restrict it so many people can log on at one time. Cable (or Roadrunner) internet service has high bandwidth and connects to a splitter that serves eight customers. If you're the only one in your neighborhood on line, you get it all. But when somebody else connects, your rate drops to half, etc. That's why cable is famous for slowing down during busy times. DSL, on the other hand, gives you a dedicated speed (slower than cable) but it doesn't change no matter how busy.
There's a whole world of internet geeks out there telling us how to ping a host and maximize the data packets to optimize speed. You can play with it by searching for "internet speed."
Hope all this doesn't sound like a wet blanket. You'll be happy. This technology is getting so cheap that I can't see why everyone doesn't go to some type of high speed service. Even satelite TV services are offering it where land lines aren't available. Once you leave dial-up, you'll wonder how you ever survived it. 2-piper, you there?