There really isn't much of a difference besides whichever position feels more comfortable. The important thing about cock rings is they have to be applying a light pressure to the sides of the shaft. Blood enters the penis in the center, and exits through smaller veins in the sides, by restricting the flow of the blood leaving the penis it become engorged with more blood causing a longer/firmer erection.
If you are new to cock rings only wear them from a maximum of 20 minutes regardless of how it feels. As your body adjusts over time you can start wearing them for longer periods of time. Start with a cock ring you can easily remove (the one's that close with a snap are best for beginners). Metal rings should only be used by experienced wearers since they can become stuck if you don't understand the cycles of your body and penis when using them. Apply the cock ring while flaccid, not erect.
Finally cock rings just aren't for everyone, feel free to experiment, but don't think you have to enjoy it if you don't.
If you would like additional information I would suggest contacting your local sex toy store. Good Vibrations in San Francisco (Polk or Howard) have educated staff members that can supply you with more info as needed, or you can check out their GV TV segment on cockrings: http://www.youtube.com/p.swf?video_id=xbueKbFXxZY&eurl=http://www.goodvibes.com/Content--GV-TV--id-1995&iurl=http://sjc-static7.sjc.youtube.com/vi/xbueKbFXxZY/2.jpg&t=OEgsToPDskKFlyVI0rfeiPEvZFtuwGdn
Hope that helps