I recall seeing literature from Dorian or Aloris that confirmed that the wedge type is more accurate and repeatable, and I am at least 95% sure they also said it's more rigid.
I actually just ordered the Shars AXA from the eBay store for myself. The eBay store is almost always cheaper than their own site. Note that if you are ordering multiple items from them they will combine shipping. My combined order was $12 cheaper to ship than the sum of the listed shipping prices of all items. Be warned, though, that apparently the policy has changed since I last did it so you can no longer add items to your cart and request a combined total from the seller and then decide if you want to purchase based on the final total. Now by requesting the total you are committing to the purchase. I don't care for that policy, but Shars always seems to discount it appreciably.