Peerless makes your characters glow yellow-ish as the Planet's holy light is surrounding and protecting them. Only Aeris' limit breaks Planet Protector and Great Gospel can give you this status. I think you're invincible to everything while under Peerless. Physical attacks always miss and magic attacks do 0 damage. It's similar to FF8's Invincible status. Of course, you can only use the status to your advantage (SPOILER)on Disc 1. However, I used a cheat to (SPOILER)fight Emerald Weapon with Aeris in my party and had her use Great Gospel, and all attacks used by Emerald Weapon (Emerald Shoot, Emerald Beam, Revenge Stamp) and its eyes did 0 damage or missed. Emerald never used Aire Tam Storm while my party was in Peerless, so I'm not sure how well Peerless blocks that. I'll also have to try (SPOILER)fighting Safer Sephiroth with Aeris again and see if Peerless causes even Super Nova to do 0 damage.

Shield isn't the same as Peerless. Your characters won't be glowing, and the status lasts for a lot shorter time than Peerless. Shield also doesn't protect you from stronger magic attacks (read: useless in the final battle), it takes loads of MP and it can only be cast on one person at a time. Use Aeris' limit breaks for Peerless instead, and when you can't use them anymore, use Big Guard, that protects your party from all kind of attacks, lasts longer than Shield and gives everyone Haste too.