I've got a RPi 3B running Lakka. I find it to be a more reliable solution than RetroPie. I haven't used Batocera. The Lakka RPi 3B is one of my secondary emulation rigs, setup in the bedroom with wireless 360 controllers.
My latest primary emulation machine is a Lenovo Thinkcentre M93P with a Core i5, 8GB, and a SSD. I bought this reconditioned from Amazon a few months ago for $148. It blows away the RPi and runs pretty much everything.
I considered a RPi 4 but the RPi solutions have gotten a lot more expensive than they used to be. Long story short, when I priced the RPi 4 solution with power supply, fan, SSD adapter caddy, and a decent case it was more expensive than the Core i5 Lenovo M93P.
The Lenovo came with Windows 10. I could have installed Lakka but Windows runs RetroArch and almost every other emulator and front end ever made. I figured there was no point restricting myself to Lakka when I can have it all.