There are 2 things involved with radios that could possibly change how you drive. Neither is likely to make a huge difference in today's market unless you're literally on the very edge and doing every lap exactly the same.
1) latency time
2) latency jitter
Latency time is the time it takes for your change at the controls to be sent to the servo/esc. For most equipment today, that number is generally very low for just about every major brand.
The jitter is the difference in that latency. Good equipment will have a consistent latency, such that it is always the same, so you know as you come into a corner, that this is the timing you start to turn. Bad equipment will have really low latency one time, and higher latency the next, such that you turn different even if you as the driver do exactly the same thing both times.
Spektrum has a reasonably quick writeup on this here:
http://www.spektrumrc.com/DSM/Technology/latency.aspx
You said you have a Spektrum Dx2s, which already uses the same radio technology as found in the Dx3R Pro. So, buying that upgrade won't help you for that reason.
If, however, you find the Dx3R Pro more comfortable to hold, or you want to use the telemetry features that you can display on those, or you need to bind to many receivers (run more than 5 vehicles)...then the Dx3R Pro (or the older non-pro) may be beneficial for you to pick up. As far as the technical radio aspects though, nothing in their current lineup will make things better, or worse, for you.