Action Points have a better defined benefit.
They give you an attack. This attack boosts your chance to hit and to deal damage in a round. They allow you to exploit a limited tactical advantage a lot better then just a +1d6 to hit would do.
You get your attack bonuses from gaining combat advantage or from your leaders (and "leadery" allies), or both. Action Points allow you to exploit a short term benefit granted by the tactical situation.
For example, a Fighter uses Come and Get It to bring several opponents close to himself. This might be one of the few moments where he actually has this many opponents around him. It might be the right moment for spending an action point to use another Close Burst power.
Alternatively, the Warlock just used that power that gives 10(+INT) Vulnerability to an opponent - now might be the time for others to spend their action point to get the chance to add this damage twice.
Or some Leader just gave you a +2 bonus to your next attack rolls, and you have combat advantage! Maybe you spend an action point _now_ to use two of your better powers, increasing your chance to deal significant damage.
Or your Wizard is Dazed, and he is currently sustaining a power. He could do nothing excepting sustaining the power, but a bunch of enemies are within range of one of his area bursts - maybe this is the time to spend an action point to sustain the power and use this opportunity.
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4E Action Points involve more tactical thinking. Their benefits are a lot more situation dependent then a +1d6 you can give one of your attacks.
Also it might be notable that the 3E style action point doesn't work so well for attacks that target multiple enemies. If it applies only to one of the attack rolls, it is a weak effect. If it applies to all, when do you make the decision? How can you make the decision? The situation where most or all of your attacks fail (but only in a way that a +1d6 can turn this around) will happen a lot less then on single attack rolls. If you roll multiple attacks for a power, it's more likely you get a distribution of hits and misses. Even if the benefit applies to all attacks, you get less returns as if you had made only one attack.
That might be another aspect. A 4E Action Point involves a little less gambling - of course you don't know if your attack(s) on your extra action (assuming that's what you will be using them for) will hit. But whatever you do with that extra action, the benefit will be proportional to the power itself.
Humans can actually get a +3 bonus when spending action poins - and it applies to all of their attacks.
(You might note: Elven Accuracy and Wand Accuracy have similar problems - they affect only one attack. What we should take from that: Both abilities are designed for the type of character with single-target/single-attack powers!)