For minimizing star trails and capturing a stronger Milky Way exposure, use the faster lens: 17mm at f/2.8.

The 10mm lens gives a wider field of view, so you can fit more sky into one frame, but that does not make it a “brighter” choice. The key tradeoff here is field of view versus aperture. A wider focal length can tolerate a longer shutter before trails become obvious, but f/2.8 lets in much more light than f/4.5, which is usually the bigger advantage for Milky Way work.

So if your priority is the cleanest single exposure with less need to push ISO, the Sigma at 17mm f/2.8 is the better option.

Choose the 10mm only if you specifically want the extra-wide perspective in one shot. If you’re willing to stitch multiple images, the wider lens matters less because you can build a broader view from several frames shot with the 17mm lens.