I've now done a first round of testing, comparing the Sig Kilo 2000 to a Leica 1600 under a variety of conditions. Further testing will be done.
The primary advantage of the Leica is slightly better optics. To me, they are clearer, sharper, and brighter. If I had to carry only one optic being a rangefinder and no binoculars the Leica would have the edge.
Accuracy is virtually identical to the Leica. I was ranging objects in the 1500 yard range, and the differences were within a couple yards.
Ranging distance: the Sig is better. I could easily range reflective objects in the 2300-2500 yard range with the Sig. I've had readings with the Leica in the 1800-2000 yard range, but they're rare.
Speed: the Sig is clearly superior, providing instant readings when the button is depressed and it updates very quickly.
Reading the display: I have no problem with either. The digits in the Sig are slightly larger and appear to be a bit brighter. There is a brightness setting; I used "auto".
Readings in weather: this was the primary reason I was interested in the Sig. The Sig is better. I was able to range objects in fog further than the Leica, every time. I was also in snow and the Sig ranges better in snow.
There is a caveat: I was testing the Sig in "Best"mode, which provides a reading of the strongest returned signal. There is a "Last" setting, which returns the distance to the further object it receives a returned signal from. I wasn't aware of that setting when I tested this weekend. I quickly tested the "Last" setting this morning in woods behind my house. On "Best" the distance came back as 18 yards: the distance to the closest branch. On "Last" I got 52 yards: the distance through the brush and branches to the house beyond the woods.
In my snow testing with the unit set to "Best" I would get readings that toggled between +/-30 yards and +/-300 yards: 30 to the snow flakes, and 300 to the distant object. I suspect if I had set the rangefinder to "Last" mode in the fog and snow it would outperform the Leica by a greater degree because it would ignore the closer readings off the moisture.
Size and weight: comparable.
I am speculating, but my guess is that the Leica is programmed more conservatively. If it does not receive a strong signal from a certain distance, it won't provide a reading. It errs on the side of caution. It may also be that Leica deliberately limits distant readings by modifying the program to accept certain distances. I truly believe that the 800, 900, 1200, and 1600 had virtually identical components, but were programmed with limitations as "planned obsolescence" to prod people to buy the newer products as they came out. When the Leica 2000 comes out, we'll see.

Settings: I tested in "AMR" mode: "Angle Modification Range". This is the horizontal distance to an object. There is a "LOS" setting which provides the actual Line Of Sight distance. I'm a rifle hunter so the advantage of using angle modified readings is of little value to me, but why not use it.
Conclusion: the Leica has slightly better optics, but not enough better to justify it over the Sig. I have not found any other advantage to the Leica. The Sig clearly outperforms the Leica in ranging capabilities. For $415, it's a steal.