The type of photography that you are planning to use is an important decision factor. Here we have evaluated the Leica SL 70-200 F2.8 and the Sigma 90mm F2.8 DG DN C for their suitability to various photography scenarios:
Size and Weight Comparison
The size of a lens is a crucial factor to consider when comparing two lenses. Leica SL 70-200 F2.8 is the longer of the two lenses at 207mm. The Sigma 90mm F2.8 DG DN C with a length of 60mm, is 147mm shorter. Besides being longer, the Leica SL 70-200 F2.8 also has a larger diameter of 89mm compared to the Sigma 90mm F2.8 DG DN C's 64mm diameter.

Leica SL 70-200 F2.8 vs Sigma 90mm F2.8 DG DN C Lenses Size Comparison
The weight of a lens is equally significant as its external dimensions, particularly if you intend to handhold your camera and lens combination for extended periods. Sigma 90mm F2.8 DG DN C weighs 295g, 80% (1245g) lighter than the Leica SL 70-200 F2.8's weight of 1540g.
Filter Threads
The Leica SL 70-200 F2.8 has a filter size of 82mm whereas the Sigma 90mm F2.8 DG DN C has a 55mm diameter. Larger filters are generally more expensive than the smaller ones given all the other features are equal.
Below are links to the 82mm filters that we recommend you to consider for the Leica SL 70-200 F2.8:
And these are the 55mm filters that we recommend for the Sigma 90mm F2.8 DG DN C:
Lens Mounts
Both the Leica SL 70-200 F2.8 and the Sigma 90mm F2.8 DG DN C has the same Leica L lens mount. Some of the latest released cameras that are compatible with the Leica L lenses are Leica SL3-P, Panasonic S1 II and Panasonic S1 IIE.
Sigma 90mm F2.8 DG DN C is also available in Sony E mount.
Focal Range
Leica SL 70-200 F2.8 has a focal range of 70-200mm and
2.9X zoom ratio . When it is mounted on an APS-C sensor camera with 1.5x crop, it provides a 35mm (FF) equivalent of
105 - 300mm.
On the other hand, the Sigma 90mm F2.8 DG DN C is a prime lens with fixed focal lenght of 90mm. When it is mounted on an APS-C sensor camera with 1.5x crop, it provides a 35mm (FF) equivalent of 135mm.