The potential advantages are an increased turnout and quicker, more accurate counts.
The downsides are too numerous to list, but the principle disadvantage is that it makes electoral fraud trivial. The most important aspects of a ballot are the ability for the elector to make a choice and verify that the choice was recorded correctly. In the present system the verification is made possible by simply re-reading the ballot. In a larger sense, it's possible by becoming a scrutineer, and by the assumption that the large political parties won't collude in fraud.
If voting was electronic neither of these would be possible. It would not be possible to tell if an individual computer had been suborned by a third party to appear to record a vote for one candidate but transmit another. This is well within the abilities of a single member of the public.
If an electronic voting algorithm was used to shore-up the counting-side verifiability then that algorithm would need to be able to be updated and modified quickly, potentially delaying votes, in order to maintain a secure ballot.