use Bourne or Bash to run a Bourne script?

beliavsky_at_aol.com
Date: 05/22/04 

Date: 22 May 2004 14:44:43 -0700

Suppose I have a Bourne shell script that will run with either

#! /bin/sh

or

#! /bin/bash

on the first line. Is there a reason to prefer running it with the
Bourne or Bash shells?