if you're using the internal signal processing for scaling then the amount of lag from the input type is highly dependent on the display itself. However in most (not all) cases if you're providing a signal in the native resolution of the display VGA will be faster, even on an LCD or other modern display (I've tested this myself on my DLP projector).However with an TV/LCD monitor with VGA input the monitor will have to convert the analog signal to digital and then scale it. The lag introduced here is highly dependant on your monitors scaling engine.
I'd speculate that it's due to the fact that most of the time digital signal comes through encrypted (HDCP) so in general your display has to wait to receive the whole frame then decrypt it before it can process and display it. meanwhile VGA is streamed pixel by pixel so as long as the image processing is designed for it and the refresh rate is in range it can simply stream the image "live".
It's worth noting that most LCD based arcade machines use VGA even for modern HD panels and in setups where both the game board and the display support digital video.