The burglar blew open the safe with the dynamite and made off with the loot
is easier to process after the context sentence in 1
Once inside he saw that there was a safe with a new lock and a strongbox with an old lock,
because this context sentence introduces just one safe (as well as one strongbox), and the sentence in A refers to one definite safe (the safe).
On the other hand, sentence B
The burglar blew open the safe with the new lock and made off with the loot
presupposes more than one safe, because it specifies the safe with the new lock, i.e. both describes a definite safe (the safe) and gives some specific information (with the new lock) which could be taken to pick out that safe from a set of possible safes. Therefore, it works well as a sentence after the context sentence in 2:
Once inside he saw that there was a safe with a new lock and a safe with an old lock
which introduces two safes, one of which fits the specifics of sentence B.
Although sentence B would be possible after context sentence 1, the specific information with the new lock is redundant because there is no need, in the context of sentence 1, to pick out one safe from a set (only one is introduced in context sentence 1), and this mismatch can actually slow down processing.