Cheyenne IIIA is a fantastic airplane. I'd probably prefer one over the 400LS. It's also the quietest turboprop I've ever been in. The 1000 is the natural competitor.
It's been many years since I've flown one (and only a few times at that). As I recall, it flew remarkably well.
I would question the claimed speed numbers-- as I recall, it's more like a 270kt airplane, which is still not bad. I don't remember what the fuel burn is, but the range is pretty impressive.
All in all, an excellent airplane. The big issues with it, in my opinion, are support (Piper wishes they would all just go away), PT6s... and that's about it.
In sum, the 1000 is going to perform a bit better, but it's noisier and the cabin is smaller. Support for the 1000 is going to be significantly better. I'm pretty sure the 1000 will burn less fuel for a given trip, but I don't know exactly how much less.
Another close comparison for the Cheyenne is the Merlin IIIB/C. The Merlins are going to be faster and more efficient, with a similar size cabin-- actually a more pleasant cabin geometry, in my opinion, but a little bit noisier.
The final competitor in this group is the Cessna 441, which is almost certainly the best performer of the bunch. It really puts all the others to shame.
I considered a IIIA, 441, and Merlin before getting the 980. The only one I haven't flow is the 441, but everyone I know who has absolutely loved it. In the end, I didn't need, or particularly want, the big cabin of the IIIA or Merlin, and I didn't want to spend the extra money for a 441-- plus I was concerned about support for that airframe as well. Also, I have a Commander service center on my home field, and years of personal experience with Commanders.