Having worked on naval aircraft for several years and knowing something of the conduct required in such situations I take contention with almost all of what SkiBum5 has written.

...never leave anything the enemy can use...
As stated on CNN and several other major news outlets, nearly all of the classified equipment on the plane was destroyed in accordance with the squadron's Emergency Destruction Bill. All naval facilities in possession of classified materials have these and they are quite specific about what goes first, second, etc. when the materials in question could fall into the wrong hands. I find no fault with the crew in the execution of their duties in that they attempted to do just this.
However, in an environment such as this one (namely the inside of an airplane in extremis,) it may not be physically possible to destroy all of the sensitive equipment prior to landing. Most of what the crew has access to on the inside of the plane is display and data handling equipment. Radars, receivers and other such systems can usually only be accessed from the outside or via major maintenance by ground crew. The expectation that the crew could destroy all of the equipment on the aircraft is quite frankly ludicrous in this light.
With the details of the flight envelope the aircraft was in prior to landing, it is now readily apparent that the best efforts of the crew were just that, their best efforts.

The most ideal solution would be to place demolitions charges on key equipment and destroy it beyond repair as the crew abandoned the aircraft. Pre-placed charges in the external antenna housings would also be detonated. But, this equipment is not carried on-board.
Absolutely not and for good reason. Safety of the aircrew is paramount, routinely strapping on large explosive charges is not only a danger to the aircrew should the aircraft encounter an electrical storm, but also to the maintenance personnel charged with working on the P-3 airframe. Furthermore, with the casings used for various units it would require a considerable charge to obliterate each one. Now the question of how many tens of pounds of explosives should the aircraft fly around with permanently mounted in it comes calling. Impractical and extremely threatening to aircrew safety.
As a maintainer I can speak from personal experience when I say that the last thing I want on an airplane are large fixed packages of explosives. Ordnance mishaps annually claim a number of lives or cause permanent disability. It is not unknown for maintenance personnel to inadvertently activate ejection seats while seated in them, cause unintentional firings of aircraft gun systems, or inadvertently activate various cartridge actuaded devices. With that in mind I would seriously hate to see what would happen to such an $80M (USD) airframe as the EP-3E if some J. Random Airman were to press the wrong button at the wrong time.
Having sufficient explosives to destroy a radar or other major electronic system in an aircraft is also not as simple as it would seem. When electronics are installed in an aircraft two things are taken into consideration:
(1)- Location with regard for antenna/other connection requirements.
(2)- Weight and balance.
It is not uncommon to have a single system with major components placed throughout an aircraft, note that ease of maintenance is not at all a requirement. Once the airframe is designed and subsequently the engines and hydraulic lines are fitted, the electronic systems inside the airframe are sort of jammed wherever they can fit. This is not done as haphazardly as it would seem given that the aircraft must be balanced properly in order for it to fly correctly. With that in mind a four hundred pound transmitter should be mounted in the center of the airplane with it's corresponding antenna in the nose. Now not only are we placing a huge amount of explosives in the airplane, but we are distributing them throughout the airframe. One of these packages inadvertently detonating would kill n people, and I am sure the families of those people would probably be less happy about that than having them detained in a slightly hostile country.

The next best thing would be to call in an air-strike from F-117s or B-2s to destroy the EP-3E on the ground.
Personally, I'd prefer not to go to war with the Chinese if that is okay.

...a responsibility we failed to consummate...
The crew is home, no one is dead, they will not gain the collected intelligence. Therefore we did come out of this ahead, admittedly just by a bare margin. This is an airplane, the Chinese still do not know what it is that we were after or how much other information we have collected. Therefore I would call the mission a success in a small respect in that they have no idea what it was we have (in terms of previously collected intelligence,) or had onboard that particular airplane. Again most importantly, the twenty-four members of the aircrew are home safely with a hell of a story.

SkiBum5: Yes and no. The explosives themselves are very stable (if you subject 'plastic' explosives to sudden shock while they are on fire they will detonate,) however the systems that are used to activate these devices are electrical in nature. This is where the failures will start and most certainly will kill people.
The aircraft itself is a part of U.S. territory, however the plane is currently on Chinese soil. If the U.S. were to destroy the plane we would be also responsible for the collateral damage done to the airfield and the potential risks to their citizens. ' Possession is nine-tenths of the law' or so the saying goes. We need to get the airframe back, although getting the Chinese to allow U.S. military technicians/aircrew into the country in order to repair/pilot the plane is a sticky situation. They have every legal right to deny anyone they wish entrance into the country just as we do.
In a strictly tactical sense the Chinese should have shot the plane out of the sky before/after the collision and then made up whatever story they wanted to later. Second guessing accomplishes extremely few things in this situation as what has happened is already over, and it now lies in the purview of the diplomats.