Slightly higher contrast, and a few other things from Zeiss
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Very slightly higher contrast, that's what I got from the Zeiss Batis lenses when I had them. The blacks were more true to what I saw, and not a dark gray. That's the pop you get, as the purer blacks make everything else stand out a bit easier. It's pretty subtle though. At least all the Batis lenses are fairly consistent in this quality. Also tended to have good flare resistance--flaring reducing contrast a lot when it happens in any lens.
I also had the Olympus 25mm F1.2, and that was most definitely a low contrast lens (likely due to the ridiculous amount of glass in it). The lens definitely muted colors and added sort of a light gray haze over everything I shot with it. A very flat look that was noticeable, especially compared to the Olympus 12-40mm f2.8. A very flare prone lens too.
Most of these image quality things are adjustable in post, but it's nice when you have a set of lenses with a consistent color and contrast rendering so you can use a single LUT and adjust things without fiddling much for wide differences.
From what I am able to gather, it's a combination of an optimized low element lens design with superior coatings that block less light so more gets directly to the sensor with minimal alteration. That's what gives better color and contrast. Also tends to produce better resolution and gives stronger flare resistance.
However, simplifying a lens design has trade-offs. Most notably with Zeiss, their lenses tend to have a very strong vignette as a consistent character. Also with the advent of more advanced glass, their bokeh signature has developed into a harsher look, something I'm not too keen on with the hard edges and onion-rings in the bokeh circles showing up. Yeah, the Zeiss lenses, especially modern ones are very sharp, but at the expense of what other image quality parameters?
All 'normal' glass lenses, with special elements not used, tend to have much smother bokeh--characteristic of vintage glass, but it's hard to correct other flaws that may become an issue.
Still, this is mostly splitting hairs, with your lighting and PP making a much bigger impact than lens choice.