The type of photography that you are planning to use is an important decision factor. Here we have evaluated the Sony FE 85mm F1.4 GM II 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. Sony FE 85mm F1.4 GM II is the longer of the two lenses at 107mm. The Sigma 90mm F2.8 DG DN C with a length of 60mm, is 47mm shorter. Besides being longer, the Sony FE 85mm F1.4 GM II also has a larger diameter of 85mm compared to the Sigma 90mm F2.8 DG DN C's 64mm diameter.

Sony FE 85mm F1.4 GM 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, 54% (347g) lighter than the Sony FE 85mm F1.4 GM II's weight of 642g.
Below you can find the dimension and weight table of the Telephoto Prime Lenses in Sony E Mount for size comparison purposes.
Telephoto Lenses in Sony E Mount for Size Comparison
Filter Threads
The Sony FE 85mm F1.4 GM II has a filter size of 77mm 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 77mm filters that we recommend you to consider for the Sony FE 85mm F1.4 GM II:
And these are the 55mm filters that we recommend for the Sigma 90mm F2.8 DG DN C:
Lens Mounts
Both the Sony FE 85mm F1.4 GM II and the Sigma 90mm F2.8 DG DN C 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 Leica L mount.
Focal Range
Sony FE 85mm F1.4 GM II is a prime lens with fixed focal lenght of 85mm. When it is mounted on an APS-C sensor camera with 1.5x crop, it provides a 35mm (FF) equivalent of
127.5mm.
On the other hand, the Sigma 90mm F2.8 DG DN C is a prime lens with fixed focal lenght of 90mm.