With paper voting, all votes are counted by several people, with oversight and random recounts. It is _possible_ to cheat, but it would require a local conspiracy for a limited number of votes.
With electronic voting, the counting is done by machines and the mechanism is obfuscated and unverifiable. If it's working correctly, it should be perfect; but if the machines were hacked, it could be done through a network and the impacts could be massive. It would require a large conspiracy to pull off, but the number of votes that could be affected could change an election.
So in summary: paper voting = higher chance of small irregularities, with limited impact; electronic voting = lower chance of massive irregularities with election changing consequences. In paper voting, the trust is distributed, while in electronic voting, it is centralized.