What are the changes between BLtouch 3.0 and 3.1? I couldn't find a reliable source listing the improvements of BLtouch 3.1 vs 3.0.
I can see that BLtouch 3.0 is sold (original) for about 20 Euro, while 3.1 costs about 30 Euro. The difference is significant.
What are the improvements?
Best reference would be the original equipment manufacturer (Antclabs). It appears their sensor has had many versions:

So, from 3.0 to 3.1 is a software upgrade. Reported highlights are:

★ Smart V3.0 (Mar. 2019 ~ ) : S10, S60, S90, S120, S140, S150, S160,
PWM Wiring defect indication(Blue LED), QR, Molex 1.25, Plastic
Push-pin(PC), Power Wiring defect indication(Red LED)
★ Smart V3.1 (Mar. 2019 ~ ) : S10, S60, S90, S120, S130, S140, S150,
S160, PWM Wiring defect indication(Blue LED), QR, Molex 1.25, Plastic
Push-pin(PC), Power Wiring defect indication(Red LED)

If you look at the manuals you will see the differences:
V3.0

V3.1

As can be seen, timings are different and more PWM position G-code options are available in the V3.1.