Illustrator's "Average" function is a kludge. Pretty worthless.
First of all, it's annoyingly buried in the "Object" drop-down menu and on a fly-out from that (along with a lot of other functions that might be better represented on a context sensitive tool bar).
The Average function does not allow the user really any control at all on where the anchor points will end up being aligned. The result is just "averaged" in the middle at some random place along whatever axis was chosen.
By comparison, you can shift+click individual control points on an object in CorelDRAW. The last node selected with the shape tool will remain locked into position. When using a node alignment function any other nodes that are selected will be aligned to the last one clicked, for a far more predictable, far more controlled result.
On top of that, it is often difficult just to get Illustrator's direct selection tool to only select the anchor points you want to have aligned. Very often, it over selects a bunch of other parts in the path and gives the user a bunch of aligned garbage, so you get to undo and repeat the stupid procedure until the filter does something that sort of seems correct.
A couple versions ago, Adobe FINALLY added an object lock metaphor to object alignment functions. Their solution is still a bit odd (you have to click the one object you want stationary one more time before hitting an alignment button, instead of the lock simply referencing the first or last object clicked like Flexi and Corel does). Up until then, its alignment functions were just as random as that average function (and just as good at getting me to fire up CorelDRAW to complete a certain task).
Illustrator and Freehand have both often been described as being more "elegant" than CorelDRAW. There's nothing elegant at all in having to fight with software to get it to do something pretty simple. My only interest is completing artwork. I have no loyalty to any application in getting that job done. But I think Illustrator is long overdue for improving its basic functions. IMHO, it has been getting sidetracked by parroting features from Photoshop, InDesign, ImageReady, etc.
I'm hoping IllustratorCS3 will have something far better with respect to anchor point selection and alignment. The current, long-standing implementation stinks.