If your tiles are cached, then they will be MUCH quicker than rendering a large random image on the fly.
If not cached, then the tile images will need to be rendered on the fly by the server. In this case, rendering a single large image may be quicker than rendering a lot of small tile images. BUT tiled images may still seem quicker, because it may render a few of them to appear on screen while working on the rest. Whereas with a single large image, even if it is slightly quicker, you get nothing at all on screen until ALL rendering is complete.
So tiles are generally either quicker, or seem quicker. But depending on your needs a single image can be more visually appealing as it may have better label placement (instead of all the labelling decisions being based on small areas - although there are settings that can improve this on some tile services).
But of course there could be other factors at play in each situation and you should try it out compare the results on your own particular system.