In both roles, online ordering was worlds better than a phone call.
As a Domino's employee, it was a lot easier and faster to get an order from the online system. It was often more accurate too. We didn't have to ask the drunk customer to repeat their order multiple times, then have them rage at us when we delivered what they ordered, only to find out it was not what they thought they were ordering.
As a customer, it's faster and more efficient to order online. I can save a custom order and have my really weird Frankenstein pizza ordered at the click of a button. Also, payment online is far easier and more reassuring than handing over credit card details on the phone (and don't get me started on cash).
I don't think I've ever had an online order experience any of those problems. On the other hand, I've had countless phone/human interactions that have led to order screwups, usually misspellings of my name/email/phone number despite my spelling it out for the person.
Via web..
* Ordering could easily fuck up somehow. Eg. Send multiple identical pizzas cus you pressed the button multiple times, cus the 1st time u pressed it nothing happened. I read about this actually happening recently.
* You dont get confirmation from a human.
* You cant ask questions and get answers from a human.
* You could only order what the app allows and nothing else.
* You'll probably need to register / login, forget your password, reset it, etc. etc. It will take a lot longer.
The big problem with customer service nowadays is thats it's impossible to get hold of a human you can tell your problem to, and who will hopefully deal with it (eg. google)