Both carbs work the same way and both have the same size carbs below 700 cfm. The difference is not in performance but in how they are tuned. The Carter AVS carburetor (sold under license by Edelbrock) has been around just as long as the Holley. GM uses their own brand of carbs (the Rochester 4GC which was eventually replaced by the new and improved QuadraJet), and Ford also made their own carbs (Autolite), with only Chrysler buying and using Carter carbs after 1964.
I switched away from Carter carbs back in 1962-63 as Carter didn't offer a bigger carb; and I was really tired of multiple carbs to get enough cfm. Holley had an 850 and 950 cfm carb that was much easier to tune than two Carter AVS carbs were; so I switched over. I have owned and tuned Holley's ever since. The Holley can be tuned with a screwdriver, but it can get messy as the fuel bowls have to come off to get to the jets. The Carter requires you to remove the top of the carb with all of the linkage involved it can be a hassle (especially trying to get the rods in the jets while leaning over a fender in a sandy pit area). Another stroke against the Carter is you have to bend those rods to adjust things like tip in point for back barrels and accelerator shots which is neither easy or scientific (with a Holley you turn a screw).
Some people swear by Holleys other swear at them. Out of the box if you don't do anything to them you couldn't tell what you had under the hood (Edelbrock or Holley).