there are two stages to writing things to a raid array
1. writing from the OS to the raid card
2. writing from the raid card to the drives
battery backup on the raid card makes step 2 reliable. this means that if the data is written to the raid card it should be considered as safe as if it was on the actual drives (it's not quite that safe, but close enough)
However, without barriers, the data isn't sent from the OS to the raid card in any predictable pattern. It's sent at the whim of the OS cache flusing algorithm. This can result in some data making it to the raid controller and other data not making it to raid controller if you have an unclean shutdown. If the data is never sent to the raid controller, then the battery there can't do you any good.
With Barriers, the system can enforce that data gets to raid controller in a particular order, and so the only data that would be lost is the data since the last barrier operation was completed.
note that if you are using software raid, things are much uglier as the OS may have written the stripe to one drive and not to another (barriers only work on a single drive, not across drives). this is one of the places where hardware raid is significantly more robust than software raid.