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Not logical reasoning.

Bows are easier to learn to use, therefore bows make more sense. They also have the range on an atlatl - and slings have range on bows.
But that does not necessarily make bows deadlier. Dead is dead, an atlatl will kill you just as dead as an arrow - or a sling bullet come to that.

Bows are 'idiot' weapons. as in 'any idiot can learn to use one'.
Slings and atlatls require much longer training, higher skill  and more practice periods to become effective.

At the end of the day at 100 yards a long bow trumps an atlatl.

a good analogy is this...a bow is like a .223 rifle with a twenty round magazine. small, light, accurate out to a decent range. the atlatl is like a .45 pistol. limited ammo and range, but just as high rate of fire or better, just as accurate at shorter ranges, and much more stopping power.

this isn't perfect since the atlatl has nearly the effective range as most bows, and most arrows have nearly the same killing potential as darts. in my opinion it's more about user skill than it is equipment.

  I do believe the bow to be more deadly, if it is assuming that we are talking about a high poundage longbow.  One thing I will say though, is that a bow is easier to shoot accurately than an atlatl and has greater range, not necessarily that the atlatl is less deadly if it were to connect.  I would say that this would all depend who was wielding the weapons, in the right hands a bow is very deadly, and so is an atlatl, and so is a sling.  A expert slinger could easily compete with a mediocre archer in deadly combat.

This really depends. A basket shield can stop arrows fairly reliably, those things are surprisingly effective at that. An atlatl dart can get the guy standing behind it. If I had one of those, then the atlatl is a scarier prospect.

That said, you can carry more arrows than darts, so without that factor or similar, the bow is suddenly more dangerous.

A hit from an atlatl dart would be worse than a hit from an arrow. That´s what I think anyway.
Some bows from the peruvian rainforest shoots 2 meter arrows, which are capable of going through multiple bodies.

A better question is whose hands the weapons are in rather than the weapon its self.  Weapons are just objects, it's whether it's in the hands of a master.  I'd rather a bow because I've practice extensively with it.   I've probably thrown a dart less than 1000 times.

One advantage of the bow would be that it's a better ambush weapon because of less movement.  While I hope I never have to try to dodge an atlatl dart, ducking as the man throws the dart (based on the motion of the arm) would be easier than ducking an arrow as the archer releases the string.  

On the otherhand, the man with the atlatl can keep his arm cocked and ready to throw while the archer can't realisticly keep a bow drawn for more than a minute

For me, if I'm hunting a 2,000lbs  bull, I'd take the atlatl.  For a 150lbs deer, a bow.  For the neighbor's dog who digs in my garden, a sling and a tennis ball.

also, the atlatl takes a bit longer time to load, so you have some time to get ahead to more cover, dodge his dart, go to cover, dodge his dart, go to cover. he eventually runs out of darts, or your too close for him to do anything except use the atlatl as a light club.