Everything is online these days, if you have an option for your customers to pay online it will increase your credibility and will also result in extra revenue.
It just means your doors are open 24*7 for business. We offer payment gateway solutions which will help you do just this.
If you had to choose a bank, one offers branch banking and another offers branch banking and a facility to use an ATM at no extra charge the obvious choice is the latter. In addition you would assume that the bank that offers both has better infrastructure and is overall a better bank out of the two.
The choice is obvious and will be same for your customers as well.