Transfer large files beween Android device and an iPad mini I have an iPad mini and a Galaxy Tab 7.7 tablet.

What is the easiest way to transfer several large files between an Android device and an iPad device?
If you have access to a computer, it might be easier to connect the Galaxy Tab and iPad to it via USB, mount both for file access (not sure how this is done in Apple world, but most Android tablets and phones come with built-in features for accessing storage via USB,) copy the files off the source device, and then copy them to the target.

If you need to do this over wireless connection and have access to the Internet (either via cell data or Wi-Fi,) third-party apps might be an easier solution. For example Dropbox is free, available for both Android and iOS, but has a 300MB file size limit. Google Drive is another alternative, with a free 5GB storage, apps on both operating systems, with file size limit of 10GB each.  There are a myriad other similar services that are available on both platforms, but all of them require Internet connectivity, and usually an account.

For direct device-to-device transfers there are fewer choices.  AirBlue uses bluetooth connectivity on both iOS and Android devices for file transfer.  Unfortunately it's only available for jailbroken iPhones via Cydia store.  Here is another walk-through for file copying over Wi-Fi, but this requires for both Android device to be rooted, and the iOS device to be jailbroken.  Instructions from here are a bit dated, but do not require any rooting or jailbreaking of your devices, just a few apps that are freely available on Google Play Store and iTunes Store.