Yes, in the 1-party battle as well as in the 2-party and the 3-party battle, killing the main body of the 1st party's Bizarro is sufficient to win. However, in order to be able to attack the core in the 2-party or 3-party battle, you need to kill parts of the 2nd or 3rd party's Bizarro, whereas in the 1-party battle, you obviously don't need to switch. So, if you can't easily outdamage the core's constant healing of the main body (which you might not even if you kill Jenova easily, i.e. fast), you need to switch to the 2nd or 3rd party, which is supposed to make the fight harder as you need to setup more than just 3 characters etc.