I use Authorize.net and am quite pleased with it, though, admittedly, I've never used any other service.

I don't currently accept automated payments through them, though they do have a recurring payment functionality built in. I haven't used Auth.net's recurring payment system.

Before they implemented that, when I was building a service that relied on automatic recurring payments, I built a script that managed it (as the amount could vary from month to month depending on the selected features), and ran it on a cronjob.

It was quite secure as the processing server itself was firewalled from the internet (no way of accepting incoming connections, and operated from my home, away from the data center). Furthermore the data was all stored encrypted in the database (but it didn't survive on the public servers longer than 5 seconds or so). Whenever it processed the payments, it would pipe the output to a file and then to the printer for the hard copy records, resulting in daily printouts of the service.

Unfortunately, my service never went live, but the homegrown recurring payment system ran flawlessly for months (until it was decommissioned, that is).