360 DPads are gawd awful, it would be a poor choice for retro games.

Try getting a few of these Steelseries pads. I've used them with my Shield and I find them to be pretty damn good.

https://www.amazon.com/SteelSeries-Bluetooth-Controller-Certified-Refurbished/dp/B01M1GHE8R/ref=mp_s_a_1_5?ie=UTF8&qid=1536021539&sr=8-5&pi=AC_SX236_SY340_QL65&keywords=steelseries+controller&dpPl=1&dpID=41e5%2BmOhdjL&ref=plSrch