Fun? Open road or playing around hands down the stick. In heavy traffic or trying to remain civil in all conditions, auto.
Faster? Well, do you mean quick or fast? Unless you are Ronnie Sox's ghost, the auto is going to be quicker in most cases. Fast is top speed, and I'd have to give the nod to the one that has less powertrain loss (stick).
Then you mention that cost or OE is not an issue, but compare the gearing. For the cost of a switch, you could optimize the gearing, so that's moot.