The manufacturer's warranty ONLY covers defects (lots of dead pixels, something not working correctly out-of-the-box, etc.)
TEC covers all that, plus theft, and accidental and water damage. However, that all comes at a price: 1) the coverage is close to $10/month, 2) when you DO have to file a claim, they require a $100 deductible up-front, and 3) you're only allowed two claims within a 12-month period (manufacturing defects not included in that caveat, but Verizon is good about exchanges, so long as you can replicate the problem in-store).
The best coverage plan I've come across so far is Best Buy's Geek Squad Protection plan. it's either $170 up-front or $10/month (there's a benefit to paying all at once other than saving money in the long run, but I don't remember). It covers everything the TEC does, but there is no deductible, and I want to say there's no limit on claims either (haven't tested it out, and can't remember what they told me when I got my Photon Q; I've gotten better at protecting my devices in my "old" age, but I still tend to be accident-prone
). One other additional bonus that I just remembered is that with GSP, you are able to get a new device in-store at the time of filing the claim; with TEC, you're required to wait for them to mail it to you (which can take up to 3 days depending on when the incident happens).