But since both does the same cleanup and join() does it at a later stage - I think both should have the same memory efficiency

If you do:

my $a = async {
    ...
};
... some other stuff;

my $b = async {
    ...
};
$_->join for $a, $b;
[download]

Your peak memory usage may be slightly higher than if you do:

async {
    ...
}->detach;
... some other stuff;

async {
    ...
}->detach;
[download]

Because the second thread will require the process to allocate more virtual memory to accomodate the stack space for the second thread, because the first thread hasn't been joined when it is created.

Whereas, with the second snippet, the first thread may have completed before the second thread is created, and so the memory used by the first thread can be reused for the second. Thereby the total memory consumption may be a little lower. It's all a matter of timing.

If total memory consumption isn't a problem, just ignore it.

I'd still want to investigate the DBI error though. It is likely also a timing problem.