Does image size impact compression efficiency differently in different formats?

E.g., if an image is, say, 600px x 400px and the PNG format produces a smaller file size than JPG, does this hold true at any image size? If the image were 600,000px x 400,000px would the two file sizes still have the same relative proportions? Or is it possible that JPG's compression means that PNG will eventually produce a larger file size past some number of megapixels?