According to Plutarch:
A few days later Caesar entered and occupied Rome. He did what he could to calm people's fears and behaved with great moderation to everyone, except in the case of Metellus, one of the tribunes who tried to prevent him from taking money out of the public treasury. Caesar threatened to have Metellus put to death and followed up the threat of language of even greater truculence; it was much easier for him, he said, to do this than to say it. So, with Metellus overruled in this way, Caesar took what he wanted from the Treasury and then set out in pursuit of Pompey (Fall of the Roman Republic, Penguin Classics, Pg. 223).
This makes it sound like, if Pompey robbed the treasury, he didn't take a substantial enough amount to make a difference. He certainly left behind most of it for Caesar.
According to Caesar himself:
Remaining business was put at once to the Senate, and it was decided to levy troops through Italy and to make Pompey a grant from the treasury (The Civil War, Penguin Classics, Pg. 38).
The news of these events raised a panic at Rome; so much so, that when the consul Lentulus came to open the treasury, in accordance with the decree of the Senate, to withdraw funds for Pompey, he opened the treasury reserve and immediately fled from Rome (The Civil War, Penguin Classics, Pg. 42).
This could be interpreted as robbery with the Senate's consent. That said, Caesar is deeply biased, but it seems unlikely that he would tell a lie that big in an otherwise fairly accurate retelling of the Civil War.
In my opinion, based on the contemporary sources we have, Pompey took from the Roman treasury. However, he did so with the express approval of the Senate and he left the majority of the money behind, which prevented his "robbery" from causing an outrage like Caesar's did.
Pompey probably erred when he left so much of the treasury behind, but hindsight is 20/20. Maybe he overestimated how violently the people would react if they learnt he robbed the entire treasury. Maybe he didn't want to defy the intent of the Constitution anymore than he was already doing. Maybe he just felt guilty about taking money. Some sources allow us brief glimpses into the situation in Rome, but its difficult to be entirely sure about what happened and what people were thinking.