The type of photography that you are planning to use is an important decision factor. Here we have evaluated the Meike 85mm f1.8 ProvL 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. Meike 85mm f1.8 ProvL is the longer of the two lenses at 95mm. The Sigma 90mm F2.8 DG DN C with a length of 60mm, is 35mm shorter. Besides being longer, the Meike 85mm f1.8 ProvL also has a larger diameter of 76mm compared to the Sigma 90mm F2.8 DG DN C's 64mm diameter.

Meike 85mm f1.8 ProvL 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, 23% (93g) lighter than the Meike 85mm f1.8 ProvL's weight of 388g.
Below you can find the dimension and weight table of the Telephoto Prime Lenses in Leica L Mount for size comparison purposes.
Telephoto Lenses in Leica L Mount for Size Comparison
Filter Threads
The Meike 85mm f1.8 ProvL has a filter size of 62mm 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 62mm filters that we recommend you to consider for the Meike 85mm f1.8 ProvL:
And these are the 55mm filters that we recommend for the Sigma 90mm F2.8 DG DN C:
Lens Mounts
Both the Meike 85mm f1.8 ProvL 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
Meike 85mm f1.8 ProvL 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. When it is mounted on an APS-C sensor camera with 1.5x crop, it provides a 35mm (FF) equivalent of 135mm.