The map service sends an image that is rendered on ArcGIS Server to the client and the feature service sends the raw data for the client to render. You typically get better speed and can use more advanced symbology with a map service, at the cost of client customization and lack of offline use. The feature service allows for more customization on the client side and offline caching if needed, at the cost of speed and limited symbology on the web. Also, feature services always provide a better looking map export because you are using the vector data instead of a image from the map service. The pixelation of map services on map exports is even more noticable to me when using a vector basemap as the background.
One issue that I have come across with map services is if the visibility range is set at the time of publishing then the client cannot change the visibility range of the map service. At least that is what happens at ArcGIS Enterprise 10.8.1.
The great new is that the next version of the Map Viewer will support grouping feature services together in the web map. I hope this helps.
"Not all those who wander are lost" ~ Tolkien