Go with what works for you --- for your own reasons.

You'll notice, in the first part of the video, when he's demonstrating the upwards technique, that the rod (in this case mild steel) is applied *above* the flame, so that the molten material can flow *down* into the puddle. Then he moves the puddle up and again introduces more molten material from above.
So what is called the upwards way is in reality a series of many short *downward* flowing applications put together in an upward direction by heat convection when the torch heats the area immediately ahead of the downward applied material in order to push the puddle upward. So no matter how you slice and dice it, the downward direction is going to be the simpler more natural quicker technique because it "goes with the flow".

But I can think of some situations where you might need to work from down to up, and that's where mastery of the upward method will prove useful.

As to brazing, try bridging a wider opening, say 1/8" of daylight between joins, attempting both upward and down, and you'll see just what I'm talking about. No matter how you've succeeded in doing it until now, there are two undeniable facts to reckon with :
liquids flow downward,... and, the welder needs to be in control of his materials.