Both Astronomical Unit (AU) and Light-Year (ly) refer to measurements of distance, so a picture should have a scale based on the most accurate distance measurement available. At the moment, this is accepted to be the Metric System of measurement, which is used in most parts of the world outside the U.S., in which the base distance for such a large scale would be the Kilometer (km).
To render the AU vs. the ly, you could decide on the smallest unit shown in the picture. Here, the ly is vastly larger than the AU, so your base scale unit should probably be the AU. Like in smaller maps, a large unit is compressed into a smaller scale -- for example, on a road map one km will often be compressed into one centimeter (cm) so the map can be smaller. You can compress one AU (150 million km) into one cm, but that leaves you still with the problem that one ly is equal to 63,000 AU.
Instead, you should render the distances as scaled to their given distances of measurement. For example, the ly is more suited to a galactic scale, so you could show the Milky Way Galaxy with distances spelled out -- 120,000 ly in diameter, or 2 billion AU.
For the AU, you should show our Solar System, with its size of about 50 AU (to the outer orbit of Pluto) or 0.0007 ly. The size difference between the two does not lend itself well to a single image, so the comparison of two images -- with a single reference distance in each, say 10,000,000 km to scale on each image -- is probably your best bet. The converter linked below will help you convert distances, and eNotes has Wiki pages with all other relevant information on galaxies and solar systems.