The radio system matter, but only marginally
As Pops says, it's possible to fine tune. The main advantage (at my opinion) is better grip and possiblity to adjust especially throttle, and to some degree steering, so you can control throttle and steering better.
FM should be more glitch resistant, but many people do fine with AM.
Personally, I find that radios above EX-10, MX3, 3PDF etc. is overkill. Okay some of them got faster response times, but a fast servo matters much more.
So there's many things that is way more important than the radio: The car, charger, motor, battery, ESC etc., not to mention the value of a good selection of springs, shock oil, tires and spurs/pinions.
Schumacher Mi5 - Sanwa MT-4 / RX-462 / KO Propo PDS-2123 - Nosram 5600 X-treme Saddle Pack - LRP SPX Zero/X12 17,5 - Nosram Stealth Touch Evolution - MAAS SPS 9250