Thanks everyone who replied to this post. Based on what everyone had to say (and on some of my own observations) it seems that step cuts (especially asschers?), rose cuts, antique cuts, and any fancy shape with fewer (and therefore larger) facets, along with shallow cuts of any fancy shape seem to show up dirt the most.
I would also assume that any cut which has significant light leakage would show up dirt quickly too, because the leaking facets could act as window to the dirt rather than a mirror reflecting back light. But I'm no expert on these things
I'm wondering if this means that well proportioned step cuts with more pavilion steps, therefore a busier look with more scintillation to distract the eye would stay looking good for longer between cleans than a well proportioned step cut with fewer pavilion steps.
In fact, could there be a straightforward rule that says the greater the scintillation a diamond has (when combined with the right proportions for excellent light return), the better it will hold up between cleaning?
This post makes me sound like I'm too lazy to clean my jewellery, and that's not actually the case.

In fact I do like to keep my sparklies as clean as possible, but I also like the idea of "lower maintenance" diamonds for future purchases so that I am not noticing every single speck of dust or fingerprint smear after a few hours of wear.