I find the PADI iOS app to be really bad. The only useful things I can get to half work is the eCard and the shop locator, and the latter only shows PADI affiliated operations.
If the physical card is the same price as the eCard I'd suggest getting the physical card, taking pictures of both sides, then put the card somewhere safe. The app is flaky and dependent on PADI's technology. It's only really a time saver if all the certs you're going to use are through PADI. You'd be paying for something less reliable than a picture of a card while being forced to have the app on your phone. At least you can print out a copy of the card should your phone break/die/get stolen on vaction.
The eCard is a nice idea in principle, but given shops will accept a photocopy of the card and PADI ones can look you up, I don't see it being any better than a physical card unless it were significantly cheaper. And the QR code is an interesting idea but you're almost certain to have to fill out a bunch of paperwork when you go to a new store anyway so I don't see it being a huge time saver.
I only have the one cert/card so I don't know if you'd need to get separate cards for OW and Nitrox. The FAQ does say "Yes, you can order an eCard for each PADI course and specialty you have completed." which implies you'd need separate cards though.