After playing for some time up to level 35, I still don't have a good feeling or idea how the (B) button counter system works in multiplayer. I've been using Charge lately, because I like having an offensive measure to deal with pursuers and thought it was always 100% effective. However, two times or so, it's failed. I'm thinking it has something to do with the timing of pressing the (B) button, but... man, I have no idea. A few times I've tried to stun someone from behind and ended up getting killed in an animation where the pursuer grabs your hand and flips you over. I didn't even know that was possible.
 
I get the feeling that button mashing means you fail and the other person kills you. The game demands a lot more methodical action than mashing things until stuff happens. I've been trying to force myself to tap the (B) button once instead of hammering on it, and it's worked out so far. But still, I have no idea how this works out.
 
Anyone figured it out yet? Or heard how this stuff works exactly? I wish multiplayer had a detailed training system like the single player campaign so you could practice this stuff and the unlockable abilities.

I remember seeing an in-game message-of-the-day type story briefly talking about that.

From what I remember they said kills take priority over stun, so don't rely on them.

You really have to get to get the drop on your Hunter for (B) to work. If they hit (X) before your punch connects they will kill you, every time. The game is set to give priority to the Hunter otherwise everyone would just hide and stun. I didn't bother to read the training manual and was confused about it for a while too, I thought I was doing something wrong, or the game was lagging etc.  By training manual I mean the digital 'booklet' they included about the game as a whole, nothing unique to the multiplayer.
 
The best things to use for stunning are Smoke Bomb and Mute. Mute is a lot trickier because the effect window is 1-1.5 seconds, so you have to do when they're -right- on top of you and be quick with your stun. Smoke Bomb creates that little barrier if being chased, but if you can drop it when your Hunter is close it will make it so they can't grab you, and giving you a really good shot at the stun.

Oh okay. So if pursuers hit the kill button in any time during the Stun animation they can still stab you? That makes sense. I had heard the priority thing before, I wasn't sure what that meant. I guess some of my confusion comes from that I've never been able to counter a stun and kill a target before. Maybe I've never been able to tell.
 
I have terrible timing for the Smoke Bomb, I don't usually deploy it at the right time and pursuers kinda waltz around it. I've gotten Mute to work a grand total of one time, but the pursuer and I were playing chicken in an alley all alone at the time.
 
Anyways, thanks for everyone who replied.

Kills go before stuns. Sorry to say. You need to surprise your killer to get a stun in

The only time I've had successful stuns is with a smoke bomb. But you have to be clever with them, and good players can usually avoid the smoke. Running seems to be a better option most of the time.

I'll just enforce what some people have said, you need to have the complete and utter drop on your pursuer.  The easiest way I've found to stun pursuers is to bait them in super close and smoke bomb the area.  Then, whilst they're helplessly choking, you get a free shot to stun them.  Otherwise, indecisive pursuers that hang about an area too long deciding whether you're the right target can be stunned if you get the prompt.

You'll see a O symbol (on PS3) when the person hunting you is able to be stunned.  I imagine it's the same on 360.

It's not possible to stun your pursuer just before they kill you, I think that's right anyway. If you can figure out who's after you before they find you can sneak up on them and stun them. 
Also I find it's a lot easier to stun people in the Manhunt mode as it's easier to see who's chasing you and you have teammates who can aid you in a stun.

I just smoke bomb and stun. I get at least 2 stuns a game like that, probably more.