A measurement is a form of interaction. A's interaction with the state is information that B is not unaware of. Which is equivalent to say that A's interaction is information that B cannot use. Thus, your two statements are equivalent in that the best B can do is use the information about the state that he does have to make a prediction. A practical example of this makes the situation more clear.
Consider an experiment where A measured the spin of an unpolarized particle to be +1/2 in the z-direction. B is unaware of A's measurement. B subsequently measures the z-direction spin and finds it to be +1/2. This is a reasonable from a prediction using the superimposed state (unpolarized) state with 50% probability of being +1/2 and 50% probability of being -1.2
Now consider the same situation but with B being aware of A's measurement but unaware of the result. It remains that the best B can do is still make a probabilistic prediction.
Now consider the same experiment repeated over and over again. On B's measurement after A's measurement, B will see that 50% of the time the particle is +1/2 and 50% of the time the particle is -1/2. Thus, to B, the state is a superposition as expected. However, if A were to join B on the subsequent measurement and tell B of his early results, then B could use the collapsed state and predict the correct spin 100% of the time (since A already measured it). But, both predictions accurately conform to the results of the experiment, however one prediction (A's prediction) contains more knowledge about the system.