Battles

Location ; The Forest of Death. 
 
Both are serious. 
Winner by Death. 
No prep. 
Both start 23 Feet Apart. 
Both standard weapons. 
Who wins?
     
  

I'd say Zabuza wins.

@SpeedForceSpider: I don't rate Asuma particularly highly whereas I see Zabuza being at around about Kakashi's level and he was able to match Kakashi in all aspects (seal speed, movement and strength) in their first fight. I believe Kakashi is better than Asuma and therefore Zabuza should also be better than Asuma.

Ash pile burning isn't that great, it could be easily avoided. Zabuza on the other hand has techniques that can cover the entire battlefield in his mist and I think without the sharingan to help him out like it did Kakashi, Asuma will fall quickly.

@SpeedForceSpider: His mist is impressive, it's the reason why Kabuto focused on protecting Edo Zabuza, even going as far as sacrificing other Edo ninjas in order to do so. As well as this, it's not something that can be blown away easily, Zabuza is able to summon the mist without any water source nearby so can just make a new one easily if needed. Like I said before, without having the somewhat pre-cog the sharingan provides, I don't see how Asuma can keep up with Zabuza in the mist.

As for taijutsu, I would rate Zabuza higher than Asuma. Speed wise he can easily keep up with Kakashi and strength wise he can swing his sword around like nothing with one arm and throw it around with ease, whereas Suigetsu struggled to hold the sword with both arms. He was also able to hold Kakashi off with just one arm.

I would put my money on Zabuza.

Would also have to agree with Zabuza pulling a win here. With Asuma lacking Sharingan and versatility in battle tactics like Kakashi, he'll be at a much bigger disadvantage in this fight when Zabuza makes use of his mist jutsu and obscures the visibility of the terrain for Asuma. With Zabuza being a skilled user of stealth and deception, he could dispatch Asuma quickly while his mist jutsu was active.On top of this, Zabuza's water jutsu is capable of covering larger and wider areas than what Asuma's been shown to cover with his attacks. I don't picture Ash Pile Burning helping Asuma out here as either Zabuza can evade the attack or counter with any water jutsu, considering fire jutsu is weak against it.
 
And I don't see what wind jutsu would be able to accomplish against the mist considering attacks of the element are more focused on use of precision and force to inflict cutting and slashing damage on a foe instead of clearing out any obstructions like one could do if they were an Airbender from Avatar.