Yes, eregi() should only be used when you want to use regular expressions. Now, preg_match() is now used in favour of ereg() and ereg(). In this case, strpos() can directly replace eregi(), but you could also write:
preg_match('/[<>]/', $field)
That said, making a script die due to invalid input is a very rude way of handling user input errors. You should either inform the user that there was invalid input and request that it be refilled and resubmitted, or silently handle the invalid input (e.g., strip_tags() or htmlentities() ).