The trade off is you get more damage with the blade, and early on 10 makes quite the difference.
300 HP sustain + 10 AD
80 HP + 5 HP per AA + 10 AD
=> you need 44 AA to get the same amount of sustain (but you don't get any control of your sustain with Dorans, so the first 10-15 AA could be worthless for sustain).
That means around 9 waves (5 CS per wave) and 4.5 minutes (6 minutes into the game).
If you lose one trade early with Dorans, you can't reg back easily, cause you need to AA. So a Dorans start can easily snowball the enemy into a decent advantage.
Pots are safer.
That was always the problem of Dorans. Less sustain and you need to be active for it.