Does this edge mean that it takes longer to get "drunk" or does it mean you can still get drunk with the same amount of alcohol but it takes longer to get "smashed" and get alcohol poisoning?

If it's the former and takes longer to get "drunk," what then is the benefit of this edge?

Klaak

Great spirits have always met violent opposition from mediocre minds.
-Einstein

It takes longer for alcohol to penalize you, while not reducing the benefits (if any) you would receive for that level of drunkenness.