What chart did you get? Most, if not all, SQ charts contain blends, so 1-over-1 will not work, unless you intend to do one leg of the stitch in one color, and the other leg in the other color of the blend.
If you intend to use the above method, 1/1 on 32 ought to give you wonderful detail; the bigger you go (i.e. doing 4 stitches per) would make it lose detail, make it look more pixellated.
The smaller your stitches, the more detail you will have, so the 18ct would be smaller than doing it over two on 32 (=16ct). If you do four per square, that will cause it to lose detail, making what would've been individual stitches look blocky, especially if you have one color surrounded by other colors - 4 stitches in that one color would make it stick out, and cause it to lose the ability to blend in with its surroundings.
I'm not sure I'm explaining it well - you might need to do a tiny sample - find a part of the chart that has the most going on, such as in her face, possibly around her eyes.
Also, I'm not sure how big Mona Lisa is, but if you were to quadruple it, would you be able to find a big enough piece of fabric? I think you will have perfect detail if you do this on 18ct and it won't be bad on 16/32, if you like the coverage you get with 2 strands. On the 18, you'll get better coverage. Let us know what you decide.
I agree with Rife, if it's detail you're after you're better off going with a higher stitch count than trying to do something as laborious as doing 4 stitches per charted square. And your result will be better too! I think the 1 over 1 with alternating top and bottom colours could be a real option for you too though if you're prepared to put in the extra time.