I'm wondering if the following is equivalent?

No, they aren't equivalent. If retrieve dies, then in the first snippet, nothing will happen, as the program has terminated before the reaching the die. In the second snippet, it will print the messages, as the eval captures the die. OTOH, if retrieve doesn't die, but returns a false value, the first snippet will die, showing the message, where as the second snippet, the eval blocks return true, and neither the prints, nor the exits will occur.

Evals do not replace dies. In fact, you would use eval in combination with a die. In fact:

sub sub_that_may_die() {
    die "Oops!" if something_I_do_not_like_happens;
}
eval {sub_that_may_die()}
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is an exception mechanism. die isn't program termination, it is throwing an exception. And eval captures such exceptions. It's only exceptions that aren't captured by an eval that lead to program termination.