I always do a combination of down-shifting and braking as this saves fuel vs purely engine braking and I'm using my brakes what they were designed for; and you don't ever want to try emergency braking with cold brakes.
Under overrun conditions (e.g. engine braking - driveshaft turning the engine, essentially), a modern engine totally shuts off fueling completely, so engine braking alone is always a MPG win, as zero fuel consumption is less than idle fuel consumption with the clutch in.
Also, brakes these days are so good that you really NEED anti-lock. The limiting factor in stopping is the grip of the tire.
In the real world, just brake.
Personally, I wouldn't downshift without a rev match because of the clutch slip factor, but I was always under the impression that with the throttle closed and the engine being driven by the wheels (not by the throttle via idle), you were using virtually no fuel.
This is not how modern fuel injected cars work. Fuel consumption is determined by the ECU and is directly proportional (but not linear) to the load required to fulfill the accelerator pedal or maintain idle RPM. When the wheels drive the engine, no fuel is consumed regardless of the RPM.
Also if there is no power demand (e.g. engine RPM > transmission RPM, but RPM > idle), again, no fueling.
This is good advice for the common case of city and suburban driving, but very poor advice for mountainous terrain.
YMMV
(... sigh, couldn't resist that one)
If you need to slow down quickly enough that you're not just letting the car coast in the gear you were driving in then using the brakes to bleed some speed off isn't going to be less fuel efficient than down-shifting to a gear that will stop you in time. The engine is engaged for almost exactly the same period of time.
Assuming your car is reasonably recent, engine braking doesn't use significant fuel. See http://en.wikipedia.org/wiki/Engine_braking#Legal_implicatio....
On a slightly different note, if your rev-matching isn't smooth when you downshift to engine brake, you're just using your clutch to slow the car, which is a much more expensive part to replace than brake pads/rotors.
As for rev matching, yes, completely agreed, if you can't rev match your down shifts then engine braking is indeed going to use your clutch and that is more expensive to replace. However, if you are driving a stick shift car and you don't know how to properly rev-match on downshifts how will you easily get up the mountain where shifting from fifth to fourth to third is sometimes required simply to keep up with traffic properly? I can go from fifth at 3k to fourth at 5k without issues. Rev-matching in a stick shift is very important outside of the engine braking use case.
Why this is so, I'm not entirely sure; it does mean that you can change from manual to auto transmission without thinking (and potentially without making a fatal mistake at speed if you are pursuing a suspect). However, it just shifts the cognitive effort of making sure you're always in the correct gear (which I think is also standard advice in eg. the roadcraft system).
From a professional owner / driver perspective (eg. a taxi), the answer is simple; brakes are cheap to replace, clutches aren't.
What they really don't tell you about are things like left foot braking (which I don't do) and heel-and-toe (which I do, especially when leaving motorways where we tend to have a junction followed by an uphill slip road).
Yeah, I was used to driving my Subaru Impreza with a stick shift, then I drove my dads BMW 5-series, got into a sticky situation in traffic and had to come to a quick and sudden stop, there was no thinking involved, push the clutch and the brake was my immediate reaction... let me tell you, that BMW stopped on a dime, luckily there was no-one behind me or I'd have to explain to my dad how instinct and sheer muscle memory on my part caused someone to rear-end me and ruin his car, all because my left foot went for the clutch and caught the edge of the brake pedal...