There is a big factor that comes into play here that I should use to set the stage:
Why are big time football receivers 6'2" or 6'3" and 220lbs (think Terrell Owens), while big time defensive backs are 5'10" or 5'11" and 190lbs?
And: Why does it generally seem that DBs are the fastest guys, but you routinely see them getting beat deep by receivers who should be slower?
There are two speeds that ultimate defenders (and football defenders) have. The first is the sprint where your man may change directions, and the second is the sprint where you're going for the disc and can just go all out. Against many receivers the former is all you need, but at the elite levels you have to have the latter, and you have to be able to use it wisely. If you can stay in the ballpark with your "change direction" sprint then you've got some big challenges ahead of you. Try getting into an all-out sprint and have your man change direction and you're going to be hosed because your form is not prepared to make this change and you'll spend an extra few steps changing your vector. Receivers have the luxury of being able to be in that full sprint mode whenever they want because they know when they have to change direction and can subtly alter their form to make those changes. Defenders have to constantly be ready for the receiver to change direction.
As soon as I hear that "up" call, I try getting into the all-out sprint mode. As I'm doing that, and maybe even more importantly, I take a quick look back to see if I can get a glimpse of the disc. This quick look can give you a lot of information: what shoulder is the disc going to, is it a missile or a floater and is it flat or hooking? With this information in mind, I'll then try to close the gap, hopefully getting on the receiver's shoulder on the side I think the disc is coming to.
If I've got a bigger gap to close I might listen for a shoulder from the sideline, or try to take cues from the receiver to get some of the information the look back would have helped with. If I see the receiver really start striding I know it's going to be long and I've got to close and get by him to have a chance. If I see him sit up I can guess it's going to be a floater and I'll have time to get there and should be ready to jump. I can also figure out which shoulder by seeing how he looks back.
In the last few steps I start assessing the situation: where is the disc coming down, where can I take it earliest, where is the receiver? The goal is to take it as early as possible while not giving a bailout foul. If he's misread it, I may have a little leeway in where I can take it down or how to position myself to prevent him from making a play.
The athleticism of the opponent plays less of a role than one might think (for me at least). The first thing is to figure out where I can take the disc as early as possible. I'll generally assume that my opponent will have similar athleticism, so if I take it at my highest he should be looking to take it at a similar spot. But if I can get there at the same time or a bit earlier I'll be fine. If he's got position or can get it sooner than me, then I might have to change my bid to try to take him out of his comfort zone and hope for the best, assuming that my normal bid would be worthless.