Just remember the trade off, eggshell is easier to clean but shows more imperfections.  

Will they flex to conform to the imperfections of the existing floor or do they strain at the seams and pop?

Before installation they applied some material to smooth out any leveling imperfections.   

The thinner ones shows every imperfection in the subfloor.

All great insights already here Winn, but if you are able to oversee the painting, there are some ways to help with this often unavoidable turn over expense....For example, this time insist on some high end paint (think specialty paint store or the very best big box stuff); try a pearl or washable finish; I like one color for all the interior of all my units, ideally a white that can hide some imperfections (know and keep the code); this means no color or matching mystery later; then on the next turn over, see if you can't get away with just a wall cleaning; use a damp sponge mop with tsp or a tsp substitute  (and then rinse it with a clean water and a damp sponge mop)..not too much water, just damp.. 

You will end up painting the ceiling again as well as the trim in order to get your lines back and get rid of the old paint imperfections.  

One tenant sent me over 200 photos showing the imperfections in the house.

Stained or just poly-ed cabinets hide imperfections much longer.Painting cabinets is not expensive but it adds up and adds time to turns if you scale to more properties.

We used a bit of a darker color here which seems to hide the wall imperfections a bit more.

I always have knock down ceilings  in my rentals, look nice and they hide imperfections .Pop corn  ceilings here are a sign of a outdated, unit they must go !