Haxe supports some Alchemy opto codes that as3 does not currently support
I am not sure that 3D has found much speed increase through using them due to how they have to be used.
FastList's are faster than arrays. And stricter typing structures allow more speed.
XML parsing seems to be easier to do fast in AS3?
I really don't think though there is a huge difference between haXe and AS3 most of the time as its all ABC it probably as much down to the coder or libraries available, the real differences are when you get neko to process it backend, and don't have to re-code the classes, I mean if you change player or browser it will as lightly or not change the speed more.
With all things you need to do real experiments as theory is not the same as practice.
But if you have some real algorithms post them somebody might be able to give qualitative advice and I would not be surprised if they could be made to run faster in haxe.