The approach of eBillme does seem safer, since payment transactions are done through the online banking channel of one's bank, which limits the number of instances where one's financial information can be compromised. One issue, however, is the additional effort of making the payment yourself. It can find itself challenged by the reputation of safety of Paypal, coupled with its ability to streamline the process of one's online purchases.
Another aspect that eBillme highlights is the fact that since all of the payments coursed through them are essentially cash payments, it can be very effective in helping people to control their expenses. While this is a noble goal in itself, it somehow immediately limits the market for them. What's more, it can alienate some people who may feel that eBillme is viewing credit transactions as inherently wrong.
The entry of eBillme as another payment method provide consumers with another way to conduct their online financial transactions in a manner they deem safe, efficient, and aligned with their financial goals.