It's extremely common to hear the refrain "Oh, you have to upgrade to a 52v battery, it's totally night and day! So much faster!" and this advice is absolutely, completely, 100% bunk.
In this video I switch from a 48v to 52v battery on a RadRunner+ bike and show the speedo difference AND use a digital tachometer to measure actual wheel speed to compare the difference.
tl;dw: it's exactly as much faster as the voltage change -- a small 10% increase.
