We have this e-prescription system in Estonia for over 2 years now, nation wide.
The good - It's easier to get some recurring prescriptions that you have to take all the time, you just calle the doctor and say you are running low on the meds, he checks your previous prescriptions and can easily see that yes, you should have only a few left... (to detect you are not attempting to scam extra medicines for black market or something).
Also another good thing is that combined with an electronic pharmacy database, you can check online exactly which pharmacies currently have this medicine in stock in the right quantity(My partner takes meds that come in 10, 20, 30, 50 and 100mg forms, She only wants the 100mg ones).
The bad - Initially they had performance problems because they forgot one basic simple thing when calculating peak usage - All elderly / pension receiving people(They are also the ones who require a lot of prescription medicines.) get their pension on the same day in the beginning of the month. This gives them a reason to leave the house and go to the city, and most of them also buy their medicines within the 2 days period following it, causing a massive performance bottle-necks for that moment(This problem was later fixed by adding more servers + optimizing).