Using Image Settings, one can control the quality of individual tiles. Each tile is a JPEG-image, and the setting controls the compression-rate used to generate these JPEGs.
We did a survey of the impact of various quality settings, and came up with the following measurements. As could be predicted, reducing the tile quality significantly reduces the amount of bytes transferred:
Does tile quality impact the time it takes to serve a tile? We don't notice any meaningful difference (except for the obvious measurements directly related to physical tile file size).
Below you can see all measurements combined in a single chart: