Electronic voting machines greatly improve voting in all counties. The trick is to get proper training on the devices and to have a paper trail. Electronic voting machines must reliably print some kind of receipt that can be counted in case of discrepancies. Ballots that are scanned by machines already have paper ballots as a backup.
When using electronic voting machines the voting process is more accurate and time saving in comparison to hand counting votes. The only problem is that electronic machines can be programmed to change a citizen's vote. A great example of this is the youtube video that went viral, displaying how a person's vote for Barak Obama was continuously changed to a vote for Mitt Romney.
There will always be concerns with voting that things are being rigged, electronic or paper. Electronic transactions are easier to track, so while there will be for a good while moving forward people screaming from the rooftops their vote was "changed" or "wouldn't register" and so on, in the long run electronic machines are the better option. They are safer, whether people are ready to concede that or not is a different matter.
I think it's better to have the voting machines than to do things traditionally and by hand. It removes a lot of opportunities for human error, is faster, and allows a lot fewer election workers to handle the votes directly. People like to imagine that they lead to fraud, but voter fraud is nearly non-existent in the US, and history has shown that people can rig old-fashioned elections just as easily.
Electronic voting has a much greater chance of being incorrect since many polls have confusing formats, allowing votes not casted for intended candidates or issues.
Additionally, unless systems are "closed" not on the WWW there is always the chance that a hacker could manipulate the data, thus making it incorrect.
I believe that a hard copy vote is the best method; it may not be the fastest, however it is the most accurate.
That said, I also believe that the hardcopy vote should be bounced against a difficult database of names to ensure no double voting, etc.