Lets see, with that video I made it when warband just got released, so it was chalk full of people who were really new. They all had bad distance and timing so it was easy for me to just get in range and swing first. That isn't so much the case now. For that guy getting spammed by me, he needed to be on the attack immediatly after a parry, on the same side as my char. So at say 3:03 after his block, he kinda does nothing for a bit, while I am starting up another swing. The swing he started was right to left, even though I was on his left side.
So to hit me, right after that clank, he should have started a left to right attack, and started moving off to my right, to draw me into that swing arc. He has a slower weapon with the 2h axe so it would be sort of a tight thing. But if you watch that small section, at 3:03 or so when you hear the block noise, he should be starting a new swing right at that point. He doesn't do anything until 3:06, so while that is at slow time it is still enough for my swing to get up and connect first.
But really the idea is that you want to move away from someone's swing if possible and start your own up right away, and be able to judge who will impact first. After a bit, you can see who will hit first as soon as you click the left mouse button based on where his swing is in the animation, where yours is, and where you are both standing.
I am a ****ty battle player so I don't know what'll work well for you there, but in a tdm or something, most of the time you are probably pretty good to have a 1 hit / 1 kill weapon with range since it gives you less time you need to be playing defense. You def want a shield for ranged and cav people couching you somewhere on you too. But honestly the biggest improvement you will get is being able to block and observe timing. If you spend a moment to spectate a high scoring player on tdm that is infantry, you will see what they seem to have above most other people is defense. Many kills in TDM for me are still just a block attack back at them with pretty shaky defense. The people that are difficult can reasonably block most single swing attacks (no feints).
I am a bad shield player, but I would say the mistake I see people use with them is getting to close so I kick them, or letting me get right up to the side of them and bashing away right at the edge of the weapon sweet spot. They need to shift away from my swing arc and return swing right after I hit the shield, but also not press in too close to take a foot in the face.
So the way I take down shield users are either to wail away at that good angle, or just do 1 swing feint, most people dropping their guard when they hear the 'woosh' rather than the block impact noise.
Oh yeah Equipment wise, most defense you can get probably helps, so you can stay alive, and watch and get a feel for how people move. My main problem I have is too much aggression, so sometimes just hanging back slightly out of range and waiting and looking for openings can really help.