If you are asking from an official response, that thread covers the primary differences in design.
The truth is that the pad that is going to give you best results is going be the pad you are most comfortable using. On a personal level, 90% of the time I am using a variation of our High-Gloss pads by Lake Country.
When I first started polishing with a rotary, I used mainly 7.5 inch Lake Country Pads. I didn't know it at the time, because I didn't had purchased the pads at different site, not PAC, but these pads actually used a lower quality white and orange foam in this size.
This site only sells the high quality foam with their 6.5 inch pads, so I switched to that style and have become very comfortable with those types of pads on a rotary. I discovered the Hi-Gloss pads after I had been using the other pads for a long time. The other pads are similar in style and price but had a couple of draw backs. One, they have a sharp edge, which can increase the risk of damage to the paint and holograms. The backing Velcro material covers the entire back of the pads which means that if you rub against anything, you can instantly burn it. Also, I found the Constant Pressure foam to really make these pads a joy to use.
So the Hi Gloss Pads, on every level, are superior to previous pads I had learned to buff on. I am so comfortable with these amazing pads that I have a hard time using anything else. I should add that I have begun to use the 7.5 inch Hi-Gloss pads more as well. The reason? Because Proper Auto Care offers the highest quality foam in this size as well, unlike some others.
The Kompressor pads have a different feel, not better, not worse, but different. I will use them on occasion to change it up (and the Orange Kompressor is pretty amazing) but I am Hi Gloss kinda guy!