Sharpness The Sigma, while a class-leader in the E-mount environment, has a tougher time shaking up the Micro Four Thirds order. Performance wide open is fairly on-par, with sharpness dropping only a bit towards the outer third of the frame. Stopping down sharpens the corners up a little and performance remains fairly consistent until diffraction starts to kick in beyond F5.6.
 Chromatic Aberration Wide-open the Sigma shows fairly consistent and correctable chromatic aberration. As the lens is stopped down, blue/yellow fringing (blue line) is reduced while cyan/red fringing increases. Overall, aberrations never get to the point where corrections will greatly effect sharpness.
 Vignetting Thanks to the lens' design being optimized for APS-C use, the central part of the frame used by a Micro Four Thirds sensor is much less affected by the lens' vignetting wide-open. It continues to improve on stopping down and by F2.8 there's hardly any left.
Distortion The Sigma exudes a fair bit of barrel distortion, with its effects being most noticeable in the corners.

 Versus the Panasonic Leica Summilux DG 25mm F1.4

It is very close between these two lenses. Wide-open, the Panasonic does end up being sharper in the center all the way through the central third of the frame. However, as we move outwards, we see the sharpness of the Panasonic continues to trend downwards. The Sigma is much more consistent across the frame. That trend continues at F2, but by F2.8 the outer edges of the Panasonic have improved and surpassed the performance of the Sigma, and stays ahead as diffraction begins to lower overall sharpness of both lenses at F5.6 and beyond. So while the Sigma never beats the Panasonic, it offers a more consistent performance with sharper extremities at brighter apertures.

The Panasonic does struggle a bit with chromatic aberrations, showing a spike at the edge of the frame for both colors at all apertures. Performance near the center does seem to be consistently better than the Sigma, however.

Where the Sigma is able to pull ahead is in terms of vignetting and distortion. Vignetting hardly effects the Sigma, with only 1/3 stop of light lost at the very corners. The Panasonic, on the other hand, loses over a stop in the extremes, though it improves as soon as you stop the lens down. Both suffer from barrel distortion, but the amount the Panasonic deals with is much more than the Sigma, especially in the extremes.

It's worth noting that the Panasonic's distortion is automatically corrected when the lens is mounted on an Olympus or Panasonic camera and when it's processed with any compatible Raw converter, so we're more interested in the effect on sharpness in the corrected image.