I've used both Kahlers and Floyds since '89 and they're just different animals. I've never had tuning or stability issues with a Kahler. I do agree that the Floyd nut is better than the behind the nut lock that Kahler originally used. If think most problems are caused by not having the Kahler setup correctly. The strings won't pop off the saddles if the saddles are set high enough to maintain a proper angle and the rollers move freely. I've seen a lot of Kahlers come mounted on shims that raise the plate too high to keep the saddles up where they need to be. With behind the nut locks, tuning issues are dependent upon a properly cut nut (one of the reasons I prefer the Floyd lock). OTOH, having choices in how the nut is set up (string spacing) and the material (bone, graphite, etc.), can be a benefit, too.
For me, Kahlers seem to maintain more of a Gibson-like tone and feel. With the standard springs, they are very smooth. With heavier springs, they feel more like a Floyd and will flutter. String spacing is adjustable and intonation is much easier to set. There are more tonal options, with combinations of brass, steel, and aluminum rollers and cams. I think they're not as common as Floyds because they're more expensive to manufacture. They do require more maintenance, but not really that different from maintaining a vintage Fender tremolo or a fixed bridge.
Mostly, I think a lot of people tend to shy away from things with which they are not familiar. Having used (and still using) both, I like them both and find them to just be different tools. In general, I'm not sure I prefer one more than the other. Set up and maintained properly, they're both great!
