In out, in out, shake it all about

I’m rewriting some call centre scripts at the moment which need details about various forms people can download. I’ve been saying to fill these in (as in ‘fill in your details’) but someone else working on the same project has gone with ‘fill out your details’. This has left me in a bit of a quandary. A trip to Google tells me that ‘fill out’ is favoured (or favored) in America, while ‘fill in’ is the more acceptable version on this side of the pond. And the OED doesn’t seem to have a preference (although apparently everyone ‘fills in the blanks’). So what do you think? Are you in or out?