The type of photography that you are planning to use is an important decision factor. Here we have evaluated the Sigma 90mm F2.8 DG DN C and the Sony FE 70-200mm F4 G OSS II 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. Sony FE 70-200mm F4 G OSS II is the longer of the two lenses at 149mm. The Sigma 90mm F2.8 DG DN C with a length of 60mm, is 89mm shorter. Besides being longer, the Sony FE 70-200mm F4 G OSS II also has a larger diameter of 82mm compared to the Sigma 90mm F2.8 DG DN C's 64mm diameter.

Sony FE 70-200mm F4 G OSS II 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, which means it is 499g (62%) lighter than the Sony FE 70-200mm F4 G OSS II which has a weight of 794g.
Filter Threads
The Sigma 90mm F2.8 DG DN C has a filter size of 55mm whereas the Sony FE 70-200mm F4 G OSS II has a 72mm diameter. Larger filters are generally more expensive than the smaller ones given all the other features are equal.
Below are links to the 55mm filters that we recommend you to consider for the Sigma 90mm F2.8 DG DN C:
And these are the 72mm filters that we recommend for the Sony FE 70-200mm F4 G OSS II:
Lens Mounts
Both the Sigma 90mm F2.8 DG DN C and the Sony FE 70-200mm F4 G OSS II has the same Sony E lens mount. Some of the latest released cameras that are compatible with the Sony E lenses are Sony FX5, Sony A7R VI and Sony A7 V.
Sigma 90mm F2.8 DG DN C is also available in the Leica L mount.
Focal Range
Sigma 90mm F2.8 DG DN C is a prime lens with fixed focal lenght of 90mm.
On the other hand, the Sony FE 70-200mm F4 G OSS II 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.