This is my opinion based on my experience as a car guy and a service writer: Buy the manufacturers extended warranty every time.
Here's why ...
As a car guy: I look at it like an insurance policy. You may never need it, in which case you're just out that money. However, if you DO need it, it can save you a ton of cash and possibly some heartache. I always buy the top of the line, longest, least deductible (zero if possible) policy I can.
As a service writer: Nothing is more frustrating than having a customer past their warranty and having to tell them they need a $4,000 trans. In many cases, they just can't afford that. It might be their only car and they still owe money on it (72 month financing is so common these days). So, now they have a car they can't drive, can't fix, and can't get rid of to get a new one. So much better when I can say "You need a new trans, it's covered by your extended warranty. I'll put you in a loaner car and call you when your car is done"
Third party warranties ... depends. Anything from The Warranty Group is excellent (Car Max's MaxCare warranty is actually from The Warranty Group). They are very quick and easy to deal with and cover everything they say they will cover. On the flip side, there are some REALLY bad warranty companies. I've called in claims and found they don't cover much of anything. I called in one the other day that was limited to the current value of the vehicle (in which case, they only would cover about half of the needed repairs).