What is the biggest difference we can obtain by using these two?

The difference can be seen with Devel::Peek:

#/usr/bin/perl
use Devel::Peek;
use feature 'say';

my %assign = (
    foo => 1234,
    bar => 5678,
);
my %undef = (
    foo => 1234,
    bar => 5678,
);

%assign = ();
undef %undef;

say "%assign (",\%assign,") after assignment:";
Dump(%assign);
say "%undef (",\%undef,") after undef:";
Dump(%undef);
__END__
%assign (HASH(0x195f890)) after assignment:
SV = PVHV(0x193fe60) at 0x195f890
  REFCNT = 1
  FLAGS = (PADMY,SHAREKEYS)
  ARRAY = 0x19a1d70
  KEYS = 0
  FILL = 0
  MAX = 7
%undef (HASH(0x195f860)) after undef:
SV = PVHV(0x193fe80) at 0x195f860
  REFCNT = 1
  FLAGS = (PADMY,SHAREKEYS)
  ARRAY = 0x0
  KEYS = 0
  FILL = 0
  MAX = 7
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The difference lies in the ARRAY element of the above output. By assignment of an empty list the container of the key/value pairs is preserved, whereas undef erases it and sets it to a NULL pointer.

It is obviously cheaper to just wipe the container (and its content) instead of iterating through it and re-arranging its internal structure. - edit - see below, what dave_the_m writes.