Do you recall if any of those test were run with Option Explicit ? I don't see any mention in the thread of whether you had or not.
If you Dim and then set a regular variable immediately in code (as you would for a Const) you'll actually find the results for that should be very similar to Const as well becuase of the early type casting of the variable. Option Explicit of course doesnt provide any type casting though so doesn't help in that area anyway.
Thats my belief also, which is why I'm supporting the view of not having it in your production code to reduce the initial overhead it creates parsing the script, you've already reaped the benefits of using it during development to ensure you've correctly DIM'ed all variables. :)