I believe you, but how do you reliably check the output?

Whether using vec, pack or some other means, there are two ways: Reading the documentation, or testing experimentally on the appropriate machines.

And what does "same output" exactly mean?

For the code in Re: Displaying bit-vectors with Most Significant Bits to the left?, the topic was producing 0000011100000101 from $m0.

For the code in Re^2: Displaying bit-vectors with Most Significant Bits to the left?, the topic was producing a string consisting of the byte 0b00000111 followed by the byte 0b00000101.

I did machine programming on big-endian architectures, I don't know what to trust anymore. Do I need to check with Devel::Peek to be sure?

Check what? If pack or vec produced the expected strings? Devel::Peek::Dump would be too noisy. I'd use one of the following:

sprintf "%v02X", $bytes

unpack 'H*', $bytes
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For example,

$ perl -e'
   for my $format (qw( n v )) {
      my $bytes = pack($format, 0x1234);
      CORE::say sprintf "%v02X", $bytes;
      CORE::say unpack "H*", $bytes;
   }
'
12.34
1234
34.12
3412
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