I have a few units from Leica and Sig. It really depends what you want out of your RF. Do you want internal ballistics returns? What about expansion options outside the RF for very long range shooting? Is it for observation as well as rangefinding, or just as a rangefinder?
All that said, Leica RF's have the nicest glass and sure ranging. They are refined after their decades of experience building RF technology.
Sig tends to be bleeding edge in terms what their RF's can do. So ballistic solutions, connectivity etc. These things make quite a difference in how you use the RF...your workflow, and Sig has these figured out really well.
In terms of ranging, it depends on which RF's you are considering. Ranging in canyons at days end, my Leica 2800 could range a hair farther than my Leica 2700. My Sig 2400 BDX hit the exact same distance as my 2700, albeit it was harder to do as the Leica's sensor alignment is better. However, on a 12" cardboard target, under perfect conditions, my Leica's beat my 2400...again, it could be due to Leica's better aligned sensor such that it's easier to aim, but I think the Leica's just are better at reading those kinds of targets.
However, in rain, my Sig beat my Leicas once it got heavy.
And then there is the 3000 BDX, which so far is pounding all of them.
In your price range, between the Sigs and Leicas, I think you are limited to the Leica 2400, which lacks ballistic functions, and perhaps the 2200 BDX, which lacks some features of the 2400 BDX, but does have internal ballistics to 800 yards.
I'll tell you this, Leica glass is sweet, and the sensor alignment for aiming is very precise. They range very well in bright conditions.
The Sig ranges very well too, but feels just a hair behind the Leica when the sun is bright...usually I get it on the Leica in a couple tries....the Sig it takes a couple more...but ultimately it reads it. But that is somewhat subjective...conditions and targets really make a difference. They are close enough that sometimes I can readit with the Sig, but it takes a bit to get it with the Leica...so it's not absolutely clear. But that BDX system for hunting, if you are using the scope as well...very very fast. My son used it in January to kill 3 Aoudad rams at different distances in very short order. Would have had to dial for all three shots and so probably would not have gotten the last two off, but with the BDX system, range...fire. Pretty cool so far.