With the paper-based system you can see the ballots being marked, you can see them going into a ballot box, if you have good laws you can go watch them count the ballots, and with electronic voting all of that stuff is hidden inside the machines.
If we look at security critical systems, say banking, electronic gambling, a great deal of care is put into making those machines secure, and still problems occur. I consider electing the leader of the free world to be a more critical question than who wins the lottery.