I don't have a complete defense of each of the arguments, but I have more of less formulated a premise version of each of the arguments to my satisfcation. Any comments, critical or not are welcomed.
Conjecture: Socialism is not as efficient as Capitalism
P1 The allocation of resources is dependent on economic calculation (Proposition)
P2 Economic calculation is dependent on market prices (Proposition)
P3 Under socialism, there is only one will directing economic decision making and thus there are no market prices (Proposition)
P4 Under capitalism, there are many wills directing economic decision making and thus there are market prices (Proposition)
P5 An economic system which is more likely to misallocate resources than some other system is not as efficient as that other system (Proposition)
P6 Socialism is more likely to misallocate resources than Capitalism (From P1, P2, P3 and P4)
C Therefore, Socialism is not as efficient as Capitalism (From P5 and P6)
Conjecture: Socialism is not as Productive as Capitalism
P1 An economic system which provides a stronger incentive to produce than some other economic system is more productive than that other economic system (proposition)
P2 In a capitalist economy, individuals have a strong incentive to produce because they can keep the profits created by their production (proposition)
P3 In a socialist economy, individuals have a weak incentive to produce because they cannot keep the profits created by their production; their profits are distributed between equally between all persons (proposition)
C Therefore, Socialism is not as productive as Capitalism (From P1, P2, and P3)