Good question. This was mostly answered already, but I’ll try to put my spin on it.
There are two kinds of operation: vector and raster. If you’re familiar with Illustrator, think of Vector as a thing you can only do with strokes, and Raster as a thing you can do with any design.
With vectors, you can cut or score - score being a thin, low-power line, useful for some designs and for (you guessed it) scoring paper to fold.
With raster, you can engrave pretty much anything: vectors, strokes, bitmaps, etc. The laser goes back and forth, firing as it goes, to render a bitmap of your design.
Now, the higher the resolution of the source image the better, up to some limit (72-1000 dpi depending on settings). Images made of vectors (meshes, gradients, filled shapes, etc) are basically infinite resolution for engraving.
So, to answer your question: you would not see any difference between a vector file and a sufficiently high resolution bitmap.
There’s no quality advantage to using the gradient mesh tool vs. a bitmap (e.g. photoshop image) at high DPI.