Since I own a few guitars with both setups, here are my opinions.
2-Point Pros:
* Better tuning stability
* Easier to setup
* Greater tremolo movement
* Reliability (no need to worry about stripped bridge screws)
2-Point Cons:
* It's not as sexy as the classic 6-screw tremolo
* Not as easy to find aftermarket parts for
* The two pivots can sometimes come loose from the body
* Tone is a little less "Stratty" IMHO
6-Screw pros:
* It's got the look - it's what makes a Strat a Strat!
* Loads of aftermarket options available
* Tone - more screws = greater connection between bridge and body
6-Screw cons:
* Can be diffucult to setup
* More prone to damage due to its delicate design
* Less tremolo movement
* Tuning stability can be an issue if not properly setup
All in all I love both of them, which is why I own guitars featuring both bridges. I've come to learn a properly setup Strat can maintain very stable tuning stability whether you use the 2 or 6 point bridge. The key is keeping all the friction points lubricated.
My 2¢ anyways...