When going down a steep hill should you use the engine or brakes?

Nether what you should do is just take your foot off the gas and let it roll down the hill to its destination.

My answer:When going downhill it may be necessary to slow down to maintain steering control. Using brakes only on a long steep decline can cause the brakes to heat up and fail. Any gasoline engine or a diesel engine equipped with a "Jake Brake" can provide additional braking without heating the brakes. With many automatic transmissions it is necessary to manually select a low gear. Manual transmission drivers will do this automatically.

With 2WD vehicles there are additional considerations when using engine to brake in slick conditions:

Regardless of front or rear drive, it is usually best to cease engine braking before entering a curve. The regular brake and especially ABS will distribute braking more equally and are less likely to cause understeer than FWD engine braking or oversteer compared to RWD engine braking.