The main downside of paper ballots is the slowness and contrivance of the process. I think it's a phenomenon that's present in most countries that don't have mandatory voting law to see very low participation, especially with the younger demographic.
Having to set aside a whole day to exercise your rights as a citizen is ridiculous in my opinion and we can do a lot better. (Seeing as the article is about Switzerland, I would say their mail ballot initiative is a step in the right direction but to me it also looks less secure than paper ballots).
Another one is speed. People in this thread complain that some regions in the US only had their final counts for the last presidential election days, if not weeks after the voting ended. How is that acceptable?
In my opinion, when voting is as easy as pushing a button in an application or on a website, the democratic process will have a wider reach and could be used for many more things than the very important ones, like presidential elections or referenda (again the Swiss already do this AFAIK).