% perl -wle '
  our $VERSION = "0.1_1";
  $VERSION = eval $VERSION;
  if ($VERSION > 0.1 && $VERSION < 0.2) {
    print "ok";
  } else {
    print "not ok";
  }
'
ok

% perl -wle '
  our $VERSION = "0.1_1";
  $VERSION = eval { $VERSION };
  if ($VERSION > 0.1 && $VERSION < 0.2) {
    print "ok";
  } else {
    print "not ok";
  }
'
Argument "0.1_1" isn't numeric in numeric gt (>) at -e line 4.
not ok
%
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eval STRING and eval BLOCK do different things. In this case the BLOCK form is effectively a no-op, so the string is numified using standard coercion during the comparison, and yields the value 0.1 (plus a warning). The string form means "take this string and interpret it as a program" - and Perl code lets us put underscores in numbers, even though the standard coercion rejects them, so it evaluates as the value 0.11.

I don't know about the version->parse variant, but I imagine that PAUSE would not find a version number to parse, so the module would not be indexed correctly.