Going from a Spectrum DX4S to a current top level radio from Futaba/KO/Sanwa will probably be a very noticeable difference.
I believe this is more pronounced in the smaller the track or faster class (1/12th as example). At least I noticed a difference in SR mode on my 7PX in 1/12 and running on a a tighter, technical track. Slower class and large track with sweeping turns, maybe not so much.
As radios get faster, I think there is a point of diminishing returns (maybe we are already there.)