Does image size impact compression efficiency differently in different formats?
JPEG images can't be that big; their maximum size is (2¹⁶-1)×(2¹⁶-1). (doesn't really matter)
These are fundamentally different file formats, and their compression stems from different properties: Where JPEG is a lossy format who is able to drastically reduce the file size of content that has photographic properties (mostly: low-pass behaviour in 8×8 pixel blocks) at different levels of lossiness, PNG is lossless and compresses especially well on images with similar rows.
Thus, the size of the images depend on the content. You can't directly extrapolate from a small image to a larger version: it depends on the content of the original large image whether it compresses better in JPEG (for a given lossiness factor) or PNG.


Hence, no statement of the sort you seem to be looking for can be made, in general.

Specfically, for images that are large and that results in large swaths of identical pixels, JPEG always operates on blocks of 8×8 pixels. Even if there's a lot of monocoloured blocks, these still have to be stored and later entropy-coded in JPEG; this leads to repeating bit patterns, but not necessarily constant 0-bytes, having to go through a Huffmann-alike compressor.

In PNG, identical runs of pixels will be converted to differences to neighboring pixels; thus, large portions of 0-runs exist in large pictures with constant areas. The DEFLATE algorithm that follows this differential encoding is very efficient in reducing consecutive constant values to very few bits.