Range Extender and Powerline use different approaches to the same problem. 

• Range Extender has to be placed within range of the base router's wi-fi signal, and works by receiving and re-transmitting data, thus effectively extending the range.  It halves the data throughput (because it receives then re-transmits each packet going either way), and has a fairly large overlap of Wi-Fi coverage with the base router.
• Some Range Extenders (including your RE220) can be used in Access Point mode if provided with an ethernet cable back to the base router. Ethernet cable is much faster than re-transmitting, and removes the need for that overlap of WiFi coverage; allowing the AP to be further from the Base router and increasing the wifi coverage significantly.  This is generally the best option - but laying an ethernet cable is pretty much a no-go in historic buildings or rented apartments
• Powerline is basically an Access Point, but uses the existing electrical power wires to connect to the base router. You can place Powerline adaptors wherever there is a power socket, but the electrical wiring was never designed for data and so is not as fast as ethernet cable.  You may find (especially with a historical building) that there are several generations of electrical wiring, possibly on different circuits; and that some older wiring is sub-standard and doesn't support higher powerline speeds.  Unfortunately it's really a case of try it and see ... so I strongly recommend you ensure with the retailer that you can return if they don't work in your environment.

What I would suggest is to purchase a Powerline kit with Wi-Fi (such as TL-WPA4220 KIT or TL-WPA8630P KIT) on the condition you can return it, if it doesn't work acceptably in your house.  Plug the TL-PA4010 into power near the main router and connect with a short ethernet cable to your main router.  Place the WiFi end in the kitchen and configure, and see what the speed and reliability is like for a while.  If the Powerline is acceptable, you might like to try moving the RE220 so that it provides better WiFi coverage in another part of the house.

Alternatively you could use your existing RE220 with a non-WiFi powerline kit (such as TL-PA4010 KIT, TL-PA7017 KIT or TL-PA9020P KIT).  Again connect one unit to an Ethernet port on your main router.  In (or near) the kitchen, plug the other TL-PA4010 and your RE220 into a power socket, and connect the Ethernet port on the PL-PA4010 unit to the Ethernet port on your RE220, then change your RE220 to Access Point mode. Simples :-)

Personally I have been successfully using a TL-PA8010 KIT and a single TL-WPA4220 in 3 different rented apartments over the past 5 years. 

FYI, wifi aerials are usually designed to give better coverage horizontally (rooms next to each other) rather than vertical (upstairs/downstairs)., hence the RE220's poor signal in the room below the main router.

I would personally suggest using the higher speed units if you can afford them, though old wiring may not give you higher speed - however nobody has ever complained that the network is too fast

Don, thank you for your detailed response. I appreciate it. I will review all this and see what works. Thanks again, Cindy