I also like PayDirekt as I don't like or even trust PayPal at all. Too many stories and reports of arbitrary behavior like locked accounts, frozen balances and so on. They do what they want and there's always a man in the middle of payments.
Using PayDirekt you just have to trust your bank and payments are like "normal" transactions but without knowing bank account numbers and so on. And there's some sort of payment acknowledgement for traders but without giving them full access to your bank account as "Sofort" and other services demand. (I would never anybody suggest to use services like SofortÜberweisung!)
Though paydirekt came to the market a little bit late. But not too late in my opinion. Acceptance at online stores is growing, the usage is pretty easy and there's no third party but the banks themselves. This might be a big advantage, especially for "not so native digitals"
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And I have to add something more (again):
It's getting ridiculous to say "they start paydirekt, therefore they will not start Apple Pay". No bank, not a single one, can bet on Apple Pay only. They always have to support several services because every Apple Service is exclusive for Apple. Apple Only. You can't pay with Apple Pay without having an iPhone. You can't send someone money directly without an iPhone. But 85% of the market aren't in Apples Hands. It's an Android Market!
So what do you do? So must offer an alternative. So must offer Android payment apps, you must offer services like Apple Pay. Stop concluding, if someone announces an own Android app or paydirekt support this means they will not support Apple Pay.
Hint: boon. have their own Android payment app too.