NVIDIA has done some excellent work with Project Shield. The differences in form factor alone between Project Shield and Playstation Vita provide some key advantages for Shield. By using a full sized controller, Shield is able to make use of full size analog sticks/buttons/D-pad (rather than the significantly smaller analog sticks/buttons/D-pad used in Playstation Vita); Shield is able to seamlessly fit three high capacity and cost-effective standard cylindrical Li-ion batteries (rather than lower capacity and more expensive Li-ion batteries designed for small form factors used in Playstation Vita); Shield is able to seamlessly incorporate an internal heat sink to enhance performance and to help prevent throttling during heavy gaming sessions (whereas Playstation Vita has no internal heatsink and needs to keep GPU clock operating frequencies more limited in comparison to keep heat under control); Shield is able to seamlessly incorporate a bass reflex speaker design for extended low frequency response and lower distortion (whereas Playstation Vita needs to use a sealed speaker design with higher distortion and less wide dynamic range). Shield also has hardware that is one year newer in comparison to Playstation Vita, and is fabricated on a smaller and more advanced silicon fabrication process.
At the end of the day, Shield is rated for 5-10 hours of continuous gaming, while Playstation Vita is rated for 3-5 hours of continuous gaming. Shield is rated for 14 hours of continuous HD video playback, while Playstation Vita is rated for 5 hours of continuous video playback. Shield uses up to four A15 CPU cores for gaming (with a fifth battery saver core for non-gaming light workloads), while Playstation Vita uses up to three A9 CPU cores for gaming. Shield has a GPU with 72 total pixel/vertex shader execution units operating at a clock frequency above 520MHz, while Playstation Vita has a GPU with 64 total shader execution units operating at a clock frequency of 200MHz. Shield has a 5" touchscreen with 1280x720 720p HD resolution at 294ppi, while Playstation Vita has a 5" touchscreen with 960x540 qHD resolution at 220ppi. Shield is able to play PC games that are streamed from a Kepler-equipped PC (GTX 650 or higher on a desktop, and GTX 660M or higher on a laptop), while Playstation Vita is unable to play PC games. Shield has an HDMI output to output video to a big screen TV, while Playstation Vita has no video output. Shield uses a pure Android Jellybean operating system and is able to perform every function that any other Android Jellybean tablet or phone can perform, while Playstation Vita uses a proprietary non-Android operating system and has much more limited functionality in comparison. Shield uses a standard MicroSD memory card, while Playstation Vita uses a proprietary memory card that must be purchased separately or specially bundled as a package. Shield games are free, free-to-play, and very inexpensive games from Google Play, TegraZone, etc., while Playstation Vita games are only available on relatively expensive proprietary game cards.
I do think that Playstation Vita was impressive and innovative for it's time, but there is no doubt that Shield will provide a more powerful and flexible gaming/video/email/web browsing/social networking experience, while still allowing one to have all the benefits of a pure Android device that is synced with any other Android phone or tablet in one's possession.