Both of these can run the ESB protocol, and support one transmitter sending data to the same receiver, but please be aware that you need to write the code for the MCU to implement this on top of the ESB library. The ESB protocol itself is quite simple, and you need to add code on top to implement higher level protocol features (such as encryption, channel hopping, pairing etc).
In general I would recommend using the nRF52 series over the nRF51 series as it has significantly improved CPU performance, lower current consumption, and improved peripheral and radio performance.
