Reading the power description for Swinging, we learn that the material strength of your swing line is equal to your power level rank in Swinging, which is certainly good information to know. But there aren't any real guidelines for how fast you can travel by swinging, say from building to building across Manhattan - it's got to be faster than rush hour traffic, right? So Swinging probably isn't like gravity-defying Wall Crawling or Aquatic, where your movement is at the same speed as your normal human movement, only you can do it with equal ease in these different "environments".
The first place I usually check for guidelines is Dr. Axiom's Benchmarks over at the ICONS Truth, Justice and Gaming Wiki. This gave me two more options - classify Swinging speed with Leaping and Teleportation (Distance), or classify it with Super Speed and Flight (Speed). So which should it be? There are certainly arguments for both involving real world physics vs. comic book logic. In the end, this argument swayed me to classify Swinging with Super Speed and Flight:
In The Amazing Spider-Man #510, it takes Spider-Man 9 minutes and 50 seconds to cross the entire island of Manhattan which from end to end is 13.4 miles. If he continued that speed for another 50 minutes he would have traveled 80.4 miles in an hour. Meaning, he can travel 80+ miles per hour.
So referring back to Dr. Axiom's Benchmarks for Super Speed and Flight, I would assign Spider-Man a rank of Swinging 4.
So going back to the power description, does a faster Swinging speed necessarily equate to a stronger swing line? I'm not so sure about that. Below is my revised version of Swinging taking all of this into account. Please feel free to discuss and leave suggestions in the comments. Updated Friday 9/21/12 based on discussion in the comments section.
You can swing along on a line or cable to a distance equivalent to Leaping at the same power level in a single swing, or travel at a speed equivalent to Flight at half your level in this power (rounded up) by combining multiple swings; this might be self-generated webbing or lines of force, or a device like a grappling gun or lasso. Substitute your Swinging level for your Coordination, if it is higher, for maneuvers while you are swinging (including avoiding attacks).
You can also use your swing line to catch onto things at a distance equivalent to Leaping at the same power level and pull them to you rather than you to them with a successful Coordination test.
Your swing lines can be made of any material with a Strength no greater than your power level.
Fast Swing: As a bonus power, you may travel by combining multiple swings at a speed equivalent to Flight at the same power level.