You don't need a special variant of the firmware, but older versions of the firmware had some issues that prevented some devices to work correctly. Those issues have been fixed. I cannot guarantee that every Android device now works, simply because I haven't tested each and every one of them, but I do know for fact that the fixes did resolve similar problems with
some Android devices.
Since you do have one device that works with IOIO, you can check the logcat output produced by IOIOSimpleApp and look for a message describing the firmware versions on your board.
I recommend you try V3.03 bootloader and V3.23 app. If you can't upgrade your bootloader, just upgrade the app firmware and you may need to unplug-replug the USB after a IOIO power-up for it to work. If that's the case, upgrading your bootloader is likely to completely fix this (i.e. no need to unplug/replug).