Sorting my backups - RAID 1 vs JBOD?

What you read about RAID1 is correct--it only protects against a single-drive hardware failure, and keeps you going without delay in that case. If, however, you suffer data corruption, a file gets accidentally deleted, or the controller fails, RAID1 is no better than a single drive. It's really mostly useful to people who need more uptime--for example, at work we run a RAID1 so that if a drive dies there's no visible problem form the user perspective while I get a replacement. But it's ALSO backed up to a separate drive, as protection for if the whole server blows up or when somebody deletes something important. (RAID1 also reads faster, if the driver you're using supports reading from both drives at once; writes are the same as a single drive.)

As for your question, JBOD in an enclosure like that with the automated backup you describe is better than RAID1, but not as good as two drives in separate enclosures. Thing is, if the drive enclosure itself blows up, it could very easily take both drives with it, meaning no protection at all. Similarly, if one drive dies violently, it could corrupt the data on the other on the same controller; this is less likely with SATA controllers than PATA ones that shared the same bus, but I've seen it happen once.

Having two separate enclosures means that if one enclosure goes bad in a violent way it's very unlikely to have any effect on the other. Not 100%, since they will be physically connected through the same computer, but a lot safer.

This is what I do at home--fast FW800 enclosure for online data, then a cheap USB2 drive for the backup, since speed really doesn't matter.

Of course, the safest thing of all is to have some sort of an offsite backup plan, to handle something like a lightning strike (which would blow up anything plugged in in the house), theft, or fire. Again, I keep a drive at my parents' house 20 miles away for just such an occurrence. That of course is a hassle, so an alternative would be an online backup service at least for critical files, though those have major speed issues.