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 55mm F1.8 ZA CZ 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 55mm F1.8 ZA CZ is the longer of the two lenses at 71mm. The Sigma 90mm F2.8 DG DN C with a length of 60mm, is 11mm shorter. On the other hand, there is no difference between the max diameters of these lenses, both coming at 64mm.

Sony FE 55mm F1.8 ZA CZ 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. Sony FE 55mm F1.8 ZA CZ weighs 281g, 4% (14g) lighter than the Sigma 90mm F2.8 DG DN C's weight of 295g.
Filter Threads
The Sigma 90mm F2.8 DG DN C has a filter size of 55mm whereas the Sony FE 55mm F1.8 ZA CZ has a 49mm 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 49mm filters that we recommend for the Sony FE 55mm F1.8 ZA CZ:
Lens Mounts
Both the Sigma 90mm F2.8 DG DN C and the Sony FE 55mm F1.8 ZA CZ 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 55mm F1.8 ZA CZ is a prime lens with fixed focal lenght of 55mm. When it is mounted on an APS-C sensor camera with 1.5x crop, it provides a 35mm (FF) equivalent of 82.5mm.