It depends what video codec the .mov files use. The video formats/codecs supported by the iPad are:
H.264 video up to 720p, 30 frames per second, Main Profile level 3.1 with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats; MPEG-4 video, up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats; Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format
There are many apps that can be used on a computer to convert a noncompatible format to one that is supported by iOS.
I deleted both of the videos with the same name and started over by going back to iPhoto and again Exporting. Nothing went to iTunes eventough I checked "Automatically send slidshow to iTunes". I now have 2 copies of this movie in my iPhoto Slide Show folder that are .m4v files. in the Export window that I get in iPhoto I have Export Movie to QuickTime movie checked.
These are my selections for the Export:
This the window I get after I check Large and export: