Why different amounts of priming sugar?

I just transferred my Berliner Weiss to the keg today and I was going to try naturally carbing it while it sat till summer. I have aways force carbed before. So I changed the type in brewsmith and it is telling me that I will need 2.6 oz of corn sugar in the keg to get the right amount of vols CO2 (2.9). But if I were to prime in the bottle I would need 5.8oz. Any idea on why there is such a difference even though the vols of CO2 are the same?

Yes, because the way you serve beer from a keg is by pressurizing it with CO2, which increases the amount of CO2 dissolved in the beer.

So the serving pressure I use will increase the amount of CO2 in solution. Then how do I know the correct serving pressure to go with the right amount of corn sugar to equal the right amount of CO2 in solution?

I think they assume a "standard" carbing/serving pressure of 10-12 PSI for that calculator, but I'm not sure to be honest.

I agree with weirdboy above. There is another factor to consider that I believe may play a role. The headspace in a full keg is going to be significantly less than the combined headspace of 50 bottles of beer. More of the C02 produced is going to be dissolved in the beer in the keg rather than dispersed over the greater headspace in the bottles.

This is just a guess, but it makes sense to me. The nice thing is that if your carbonation comes up short you can easily fix it by force carbonating. Let us know how it turns out.

Right and I would also add that adding too much and overcarbing your beer in the keg is a much bigger potential problem. I did this on a beer and was really anxious to get it on tap so I just hooked it up without checking the pressure in the keg. I ended up with beer forcing itself back up my gas line and into the regulator.

So if you do overcarb be sure to bleed off the excess CO2 before you consider hooking it up.