I love Pre-Authorized Payments.
And, NO, it is not the same amount of work as using cheques. With PAP, you preload all of your payments into the system once. From that point on, you click SEND each month, and the system takes care of the rest. You wait two to three days to get an NSF report before reconciling your statements.
Your bank will make withdrawals from other banks. You need the Tenants to sign a PAP form, regardless of which bank they use.
As for cost... I have found the larger charter banks to be very expensive, so use a credit union for my PAPs, at about 1/3 to 1/2 the cost. Unofrtunately, my own CU does not allow PAPs for individuals, so I use another one, and have them transfer that money into my prime CU accounts. Awkward, yes, but it works.