In addition, modern browsers can display vector tiles directly. Mobile and apps have a somewhat harder time with this. https://www.maptiler.com/ has a good introduction for this wrt Open Street Map.
Of course I can guess a lot of data can be removed and simplified, but still, PNG seem lighter...
Many vector tile encoders have wide flexibility in geometry simplification/removal depending on zoom layer and this helps big time with tile size. I find them to be quite nice in lower bandwidth situations because you can overzoom them and still have them look good: if you zoom in and the tiles for the next zoom level haven't loaded, the vector geometry is still able to look decent, rather than pixellated like a raster tile.
What I can tell you is that my vector slippymap XHR is requesting .pbf files, so that would definitely imply protobuffers as the wire format. Ultimately that's using t-rex and mapbox-gl.js, so... not sure if there's something intermediate. But the mapbox docs say sqlite? I'm just very confused now.
The primary standard for vector tiles is Mapbox Vector Tiles (it's an open standard), which is really just a sqlite database following a particular schema.
My own personal experience developing against both png and vector tiles over the past few months is that vector tiles are better in just about every way for the kinds of things you use maps for in apps. I expect that some dataviz applications, though, would be better served by raster tiles, since you'd end up generating a raster overlay anyways.