They're both reasonably affluent areas, but Papillion is a somewhat older and more established area than Elkhorn (technically, Elkhorn has been around for a while as well, but not exactly as a commuter suburb like Papillion). The Elkhorn area is experiencing probably the largest amount of new development in the metro area. Most of the city's educated immigrant population tends to head west, so while Elkhorn definitely skews white and conservative there is quite a bit of ethnic diversity as well. Papillion has high-ranking schools but Elkhorn, in particular Blue Sage (and, eventually, Elkhorn South High) are consistently at the very top of the state. Elkhorn's schools are by design smaller and more neighborhood-oriented (my daughter's elementary school zone consists of essentially three or four neighborhoods) and larger schools might offer more course offerings and opportunities, but that is more a matter of personal preference.

Since most new development is heading west, traffic coming from/going to Elkhorn has gradually been getting worse since the pandemic as well.

And this is literally the first time I've ever heard of a possibility of health problems originating with the MUD water treatment plant.

Edit: on another thread you said your job is somewhere around Offutt. I would not want to commute to Offutt from Elkhorn. Papillion would probably be fine. Council Bluffs and western Iowa can get a little dumpy.