I've road raced on both so I can help a little.
The tread of the KDW will tend to fall apart much more so then the Azenis under serious load. The Azenis can take a serious beating and when they get greasy (from serious temp) they stay in one piece like you'd expect from an R-Comp. I've heard personally of people using KDW's that have somewhat failed or fallen fallen apart on the track more so then the average street tire. I believe this because I was throwing chunks of tire off mine more so then most street tires would do when you push them hard. They did not however, "fall apart" or "fail" like some claim. They performed extremely well, and were extremely predictable but not as fast as the RT-615.
In the rain it is different. The RT-615 is terrible. I will not ever buy this tire as my street tire because of it. Maybe it's my car, or my camber set up, or the fact that it was 45 degree's at Road A that day but my car CANNOT drive in the rain on these tires. I had no trouble reacing speeds of 120mph on the back straight on T1R's, Contact 2's, KDW's etc. in the rain. I could not go over 95 MPH on any part of the track without the car just lifting itself off the track in a hydroplaining nightmare. These tires werely nearly new and had only done 1 autocross. My nearly slick RA1's had more grip....
In terms of life on the STREET it's going to go to the KDW. You can easily get 18-23k with no burn outs or sliding around. I have only used Azenis' on the track (borrowed from a friend) but I predict based on my brothers and cosins car with the tire they will get 9-15k. On the track, like I said, the Azenis will last much longer.
If it were my street car i'd bet getting the KDW's, even though it's an old design. They stick well, are so predictable and last longer. Also, I have race tires so their inability to hold up on the track as well and slightly slower lap times isn't an issue for me. Plus they work in the rain and I still like to haul ass in the rain.