Hi JDLee,
Great questions! I found the following article that refers to a specific troubleshooting step, but also outlines some helpful information relevant to your question(s):
iTunes: May be unable to transfer videos to iPhone, iPad, or iPod
http://support.apple.com/kb/TS1497
The iPad and iPhone 4 can play High Definition (HD) content and Standard Definition (SD) content. iPods and the original iPhone, iPhone 3G, and iPhone 3GS can play Standard Definition (SD) content. To find what video formats are supported, see the Tech Specs page, click your device's product family, and then your specific model. All HD purchases from the iTunes Store also include an iPod/iPhone-compatible Standard Definition version to accompany the HD version. When syncing an HD purchase from the iTunes Store, iTunes will automatically sync the SD video for devices that require SD content.
As outlined above, if you are looking for more detailed information the best resource will be the Tech Specs page for the specific product.
For example, this excerpt from the iPhone 5 Tech Specs page outlines the iPhone 5 supports HD up to 1080p:
Video formats supported: H.264 video up to 1080p, 30 frames per second, High Profile level 4.1 with AAC-LC audio up to 160 Kbps, 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 per channel, 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
Whereas the iPhone 4 supports HD up to 720p (excerpt from iPhone 4 Tech Spec page):
Video formats supported: H.264 video up to 720p, 30 frames per second, Main Profile level 3.1 with AAC-LC audio up to 160 Kbps, 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 per channel, 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
Cheers!
Matt M.