I've tried a couple of apps that were supposedly able to let you do that process (I was trying to do it between an iPad and an iPhone). They never worked for me. In fact, they never worked so much that I've completely forgotten their names!
However, if you want to try it, I would recommend the app iFiles ($3.99, USD). As long as the other iPad is on the same WiFi network, you can wirelessly transfer photos or files to another iDevice. They both have to have the app installed and running in order to do it, but I've successfully sent photos, PDFs, .txt and .doc files back and forth between my phone and iPad, all with the press of a button. You could also send files to your computer...
This app does a LOT more than just that, so you'd be getting more than just transferring capabilities with your money. However, it's the best I've found for transferring anything between iDevices. Maybe it's worth giving it a look?
I use dropbox... it syncs between my iphone, ipads and computers. I've gotten to the point where my dropbox is my entire documents folder because I hate having to boot up a different computer, iPad, etc. to find the file I need. Has saved me from corrupted thumb drives, computer failures, and lost memory sticks many a time. Files are pick and choose shareable too. Here's their info page http://db.tt/MjWA6Li0
I have the same problem... Tried to transfer a file to my phone. It's a samsung make but I couldn't. Finally I mailed the document to myself and then opened in my mobile mail.
I am a teacher and will have a class of kids with iPads. I am going to try and send them a worksheet over the same wifi - rather than photocopy it 27 times! They then can complete if and send it back to me. Thought it might be fun! Bump is a little clunky. Might try the app. Thanks.