They’re both reliable, the odds of either mechanism failing with the car at rest are slim. What’s not reliable is remembering to do it and making sure you did it right; doing both helps with that.
I've had the car roll when I thought the handbrake was engaged. The pull-levers aren't binary, so sometimes people don't pull them enough (I sometimes get others complaining I pulled it too far and it's difficult for them to release). Other times they seem to get warn down...I've caught people driving with them still engaged.
Handbrakes are generally shit. If you ever have a used car you will notice that the engagement point gets higher and higher for the hand brake. I've had to adjust my handbrake cable to get the engagement point back to a reasonable level, as it was hitting the arm rest and still not holding the car.
If you've ever changed tires on a fwd car and kept it in gear, you will notice you can torque the front tires far harder than the rear, as the front will be held by the engine and the rear wheels can spin surprisingly easily by your own power even when held by the hand brake.
That is not true. There are situations where one or the other could fail, especially on a hill. A car in gear can be moved. That is a way how I start an engine for example.
Also depending on weather and temperature the handbrake can fail.
> That is a way how I start an engine for example.
I’ve never seen anyone successfully start an engine from stand-still with it in gear (though I’ve seen people try). You get it rolling in neutral and only then engage the gear to start the engine without a starter or battery.
They’re both reliable, the odds of either mechanism failing with the car at rest are slim. What’s not reliable is remembering to do it and making sure you did it right; doing both helps with that.
Your engine will lose compression over time so it's plausible that it'll roll a bit without the brake engaged.