So we're just talking about intra-bank transfers? They've been around quite a while. Chase Quickpay is the worst in regards to chargebacks, from what I've always heard. BOA and WF internal transfers are more difficult to reverse, IIRC and in my experience.
The ideal, if there are bank branches in both localities, is to do a cash teller deposit. There is no possibility of reversal that way.
I would think that most bank transfers (internal transfers) would be more or less the same in regards to charge-backs. They probably need the same kind of evidence to initiate a charge-back. In my experience PayPal has a very low burden of proof for a charge-back.