<p>I'd like to prefix this question with the fact that I know virtually nothing about 3D printers, aside from the general principles of how they work.</p>

<p>I've recently seen that SLS printers have become more affordable, to the point where in a few years they might be a compelling investment. I'm mainly interested in 3D printing miniatures for painting, and as such this one:</p>

<p><a href="https://i.stack.imgur.com/tQUMO.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/tQUMO.jpg" alt="Warhammer 40k Kustom Boosta-Blasta"></a></p>

<p>For scale, the miniature is about 150&nbsp;mm long. I'm mainly worried about smaller details, such as the faces of the Gunner or Driver. Will a consumer-grade SLS printer be able to print to such level of detail?</p>

It's difficult to tell from your photo the level of detail required. A scale reference in the form of a metric ruler would be valuable. If, for example, the metallic eye on the gunner is 2 mm diameter, that would be 40 layers of 50 micron grains, allowing for substantial detail.
Consumer level SLS printers, such as the Sinterit Kit, use fifty micron nylon powder and is subject to some shrinking. This implies one can expect slightly smaller than fifty micron detail to appear.
One of our makerspace members purchased an SLS model from Shapeways. The surface is layer-free and one can see the individual granules under magnification. If you required a level of certainty of this detail, consider that you can create a model containing various levels of detail, then commission Shapeways to create it.
It's certain that they use a production level system, but one can inquire of Shapeways of the size of the powder that is used.