well, "drone" itself is much older than this new branch comming out of the metal world. Drone is pretty much exactly as it sounds... long sustained notes, usually lower frequencies, with merely subtle melodic variation. Hard to pinpoint one single "origin", as these kinds of techniques have been used in a lot of traditional music from all over the place. The digeridoo would be a good example of a "drone" instrument. A lot of 20th century "classical" music used drones as well. Giacinto Scelsi is one of my favorites... he would compose entire symphonies around a single note and microtonal inflections around it sometimes. More modern drone essentially comes paired with ambient music most of the time. That low end, continuous rumble is a drone.
As for drone METAL (often called drone doom), you can definitely thank Sunn O))) for making it popular, and it's well known they took influence from Earth as well, who might be considered the first "drone metal" band. Then there's the Melvins who were doing something pretty similar too early on.
Often "stoner metal" is tied in to the drone world. This is usually way more tuneful than drone metal, and uses essentially rock-style riffs played slowly. Usually not a lot of growling in the vocals... more of a clean sung sound. The reason it gets tied in (i think anyway) is the guitar sound. it has quite a similar guitar sound... and it is very distinct. You know it when you hear it. VERY bottom heavy, ultra distorted, sustain for days... unmistakable.
Then there's funeral doom, which is somewhat related, but the guitar sound is usually not the typical "drone" sound. We won't worry about that much here.
It's definitely not something for everyone, and there's often very little harmonic variation between the pieces. The idea behind it is more to sustain a mood than it is to carry a tune. In many respects it's something for people interested in the aesthetics of music rather than the intrinsic songwriting. I know it is for me. I like the songs because of the gradual progression of a mood, and the sonic characteristics of it.
To answer your question: I am not sure if i like Sunn O))) or khanate better. They are fairly different in their approach... Sunn O))) being (mostly) instrumental, and much more into sustaining tones. They also do not have a drummer. Khanate definitely has more "holes" in their sound. If you ask me, neither is my favorite of the style, but it's hard to really say if you'd like anything from it. The whole "drone" thing is more a concept than it is a singular style, and it constitutes bands like Jesu as well... which if you've heard sound nearly NOTHING like Sunn O))).
