I pay my credit card bills by electronic transfer for a variety of reasons: record keeping, no postage, no envelope licking, no mailing, purportedly less chance of ID theft and, 'cause I'm lazy.
But, I would not enable auto bill pay. I want to carefully look at each bill before it is paid to protect my billing error rights. I have seen too many instances where incorrect or crooked charges have been paid for many months because no one carefully checks out the bills.