One of the differences between preg_match() & mb_ereg()
about "captured parenthesized subpattern".

<?php

preg_match('/(abc)(.*)/', 'abc', $match);
var_dump($match);

mb_ereg('(abc)(.*)', 'abc', $match);
var_dump($match);

?>

array(3) {
  [0]=>
  string(3) "abc"
  [1]=>
  string(3) "abc"
  [2]=>
  string(0) ""       // <-- "string"(0) "" : preg_match()
}

array(3) {
  [0]=>
  string(3) "abc"
  [1]=>
  string(3) "abc"
  [2]=>
  bool(false)       // <-- "bool"(false) : mb_ereg()
}

Old link to Oniguruma regex syntax is not working anymore, there is a working one:
https://github.com/geoffgarside/oniguruma/blob/master/Syntax.txt

Note that mb_ereg() does not support the \uFFFF unicode syntax but uses \x{FFFF} instead:

<?PHP

$text = 'Peter is a boy.'; // english
$text = 'بيتر هو صبي.'; // arabic
//$text = 'פיטר הוא ילד.'; // hebrew

mb_regex_encoding('UTF-8');

if(mb_ereg('[\x{0600}-\x{06FF}]', $text)) // arabic range
//if(mb_ereg('[\x{0590}-\x{05FF}]', $text)) // hebrew range
{
    echo "Text has some arabic/hebrew characters.";
}
else
{
    echo "Text doesnt have arabic/hebrew characters.";
}

?>

mb_ereg() cannot match over 100,000 (100K) characters (not bytes but characters)
whereas preg_match() can over 1,000,000,000 (1G, if it's within "memory_limit").
Try this.

<?php

ini_set("memory_limit", "512M"); // <-- must be changed if you try 1G.
$length = 100000; // <-- 99999 is OK / 100000 is NG

$str = "";
for ($i=0; $i<$length; $i++):
    $str .= "1"; // <-- same result if it is a multibyte character.
endfor;

if (mb_ereg('.*', $str)):
    echo '<br><span style="background-color:lightgreen">OK!</span><br>memory_limit = '.ini_get("memory_limit").'<br>$length = '.$length;
else:
    echo '<br><span style="background-color:orange">NG!</span><br>memory_limit = '.ini_get("memory_limit").'<br>$length = '.$length;
endif;

?>

If adding ".*" at the end of the pattern returns "false" 
whereas only one "." returns "true",

Suspect the string is too long for the pattern matching.

In this case, using preg_match() returns "true" when putting ".*" 
, but adding more "$" or "\z" returns "false" as expected.

mb_ereg() with a named-subpattern
never catches non-named-subpattern.
(Oniguruma's restriction)

<?php

$str = 'abcdefg';
$patternA = '\A(abcd)(.*)\z';        // both caught [1]abcd [2]efg
$patternB = '\A(abcd)(?<rest>.*)\z'; // non-named 'abcd' never caught

mb_ereg($patternA, $str, $match);
echo '<pre>'.print_r($match, true).'</pre>';

mb_ereg($patternB, $str, $match);
echo '<pre>'.print_r($match, true).'</pre>';
?>

Array
(
    [0] => abcdefg
    [1] => abcd
    [2] => efg
)

Array
(
    [0] => abcdefg
    [1] => efg
    [rest] => efg
)

<?php

# What mb_ereg() returns & changes $_3rd_argument into
# (Just run this script)

function dump2str($var) {
    ob_start();
    var_dump($var);
    $output = ob_get_contents();
    ob_end_clean();
    return $output;
}

# (PHP7)empty pattern returns bool(false) with Warning
# (PHP8)empty pattern throws ValueError
    $emp_ptn = '';
try{
    $emp_ptn.=  dump2str(mb_ereg('', 'abcde'));
}catch(Exception | Error $e){
    $emp_ptn.=  get_class($e).'<br>';
    $emp_ptn.=  $e->getMessage();
    $emp_ptn.=  '<pre>'.$e->getTraceAsString().'</pre>';
}

echo
'PHP '.phpversion().'<br><br>'.

'# match<br>'.
dump2str(mb_ereg("bcd", "abcde")).
' : mb_ereg("bcd", "abcde")<br><br>'.

'# match with 3rd argument<br>'.
dump2str(mb_ereg("bcd", "abcde", $_3rd)).
' : mb_ereg("bcd", "abcde", $_3rd)    // '.dump2str($_3rd).'<br><br>'.

'# match (0 byte)<br>'.
dump2str(mb_ereg("^", "abcde")).
' : mb_ereg("^", "abcde")<br><br>'.

'# match (0 byte) with 3rd argument<br>'.
dump2str(mb_ereg("^", "abcde", $_3rd)).
' : mb_ereg("^", "abcde", $_3rd)    // '.dump2str($_3rd).'<br><br>'.

'# unmatch<br>'.
dump2str(mb_ereg("f", "abcde")).
' : mb_ereg("f", "abcde")<br><br>'.

'# unmatch with 3rd argument<br>'.
dump2str(mb_ereg("f", "abcde", $_3rd)).
' : mb_ereg("f", "abcde", $_3rd)    // '.dump2str($_3rd).'<br><br>'.

'# empty pattern<br>'.
$emp_ptn.
' : mb_ereg("", "abcde")<br><br>'.

'# empty pattern with 3rd argument<br>'.
$emp_ptn.
' : mb_ereg("", "abcde", $_3rd)    // '.dump2str($_3rd).'<br><br>';

?>

I hope this information is shown somewhere on php.net.

According to "https://github.com/php/php-src/tree/PHP-5.6/ext/mbstring/oniguruma",
the bundled Oniguruma regex library version seems ...
 4.7.1 between PHP 5.3 - 5.4.45,
 5.9.2 between PHP 5.5 - 7.1.16,
 6.3.0 since PHP 7.2 - .

mb_ereg() seems unable to Use "named subpattern".
preg_match() seems a substitute only in UTF-8 encoding.

<?php

$text = 'multi_byte_string';
$pattern = '.*(?<name>string).*';        // "?P" causes "mbregex compile err" in PHP 5.3.5

if(mb_ereg($pattern, $text, $matches)){
    echo '<pre>'.print_r($matches, true).'</pre>';
}else{
    echo 'no match';
}

?>

This code ignores "?<name>" in $pattern and displays below.

Array
(
    [0] => multi_byte_string
    [1] => string
)

$pattern = '/.*(?<name>string).*/u';
if(preg_match($pattern, $text, $matches)){

instead of lines 2 & 3
displays below (in UTF-8 encoding).

Array
(
    [0] => multi_byte_string
    [name] => string
    [1] => string
)

<?php

// in PHP_VERSION 7.1

// WITHOUT $regs (3rd argument)
$int = mb_ereg('abcde', '_abcde_'); // [5 bytes match]
var_dump($int);                     // int(1)

$int = mb_ereg('ab', '_ab_');       // [2 bytes match]
var_dump($int);                     // int(1)

$int = mb_ereg('^', '_ab_');        // [0 bytes match]
var_dump($int);                     // int(1)

$int = mb_ereg('ab', '__');         // [not match]
var_dump($int);                     // bool(false)

$int = mb_ereg('', '_ab_');         // [error : empty pattern]
                                    // Warning: mb_ereg(): empty pattern in ...
var_dump($int);                     // bool(false)

$int = mb_ereg('ab');               // [error : fewer arguments]
                                    // Warning: mb_ereg() expects at least 2 parameters, 1 given in ...
var_dump($int);                     // bool(false)

                    // Without 3rd argument, mb_ereg() returns either int(1) or bool(false).

// WITH $regs (3rd argument)
$int = mb_ereg('abcde', '_abcde_', $regs);// [5 bytes match]
var_dump($int);                           // int(5)
var_dump($regs);                          // array(1) { [0]=> string(5) "abcde" }

$int = mb_ereg('ab', '_ab_', $regs);      // [2 bytes match]
var_dump($int);                           // int(2)
var_dump($regs);                          // array(1) { [0]=> string(2) "ab" }

$int = mb_ereg('^', '_ab_', $regs);       // [0 bytes match]
var_dump($int);                           // int(1)
var_dump($regs);                          // array(1) { [0]=> bool(false) }

$int = mb_ereg('ab', '__', $regs);        // [not match]
var_dump($int);                           // bool(false)
var_dump($regs);                          // array(0) { }

$int = mb_ereg('', '_ab_', $regs);        // [error : empty pattern]
                                          // Warning: mb_ereg(): empty pattern in ...
var_dump($int);                           // bool(false)
var_dump($regs);                          // array(0) { }

$int = mb_ereg('ab');                     // [error : fewer arguments]
                                          // Warning: mb_ereg() expects at least 2 parameters, 1 given in ...
var_dump($int);                           // bool(false)
var_dump($regs);                          // array(0) { }

                    // With 3rd argument, mb_ereg() returns either int(how many bytes matched) or bool(false)
                    // and 3rd argument is a bit complicated.

?>

While hardly mentioned anywhere, it may be useful to note that mb_ereg uses Oniguruma library internally. The syntax for the default mode (ruby) is described here:

http://www.geocities.jp/kosako3/oniguruma/doc/RE.txt

Hebrew regex tested on PHP 5, Ubuntu 8.04.
Seems to work fine without the mb_regex_encoding lines (commented out).
Didn't seem to work with \uxxxx (also commented out).

<?php
echo "Line ";
//mb_regex_encoding("ISO-8859-8");
//if(mb_ereg(".*([\u05d0-\u05ea]).*", $this->current_line))
if(mb_ereg(".*([א-ת]).*", $this->current_line))
{
    echo "has";
}
else
{
    echo "doesn't have";
}
echo " Hebrew characters.<br>";    
//mb_regex_encoding("UTF-8");
?>