from experience I can tell you that the difference can be minor to major. On two meters I have the ability to switch polarity from LH to RH circular polarization. I have heard differences from ZERO to ~ -30db . . . . . . I am not currently set up on 440 mhz to switch but should be soon. As an example : AO 7 will switch polarity on you depending on where it is . . . Western passes for me indicate that receiving on RH is better but normally LH is used on AO 7. DO64 is a strange ( interesting ) bird as it changes and changes back as it goes from one end of the horizon to the other. I have never made a QSO on DO64 because I have only listened to it when it has been in the beacon mode . . . again DO 64 is 2 meters and I am only receiving where I only have the ability to switch senses.
The difference between all vertical and all horizontal is 3 db difference. So if you are using a vertical antenna and the station you are copying is using a horizontal you will be 3 db down . . . . circular polarization is used to mitigate the fading that you will get with using straight vertical or straight horizontal BUT the kicker is that if you are on the wrong SENSE (that is the terminology to differentiate) then the down side is up to - 30 db down . . . . so with circular polarization the downside can be a lot bigger but nil fading . . . .
I hope this helps
Jim W9VNE