What items are mutually exclusive between worlds?

As of 1.2, some features are mutually exclusive between worlds. In the case of ores at least, these seems to serve as functionally identical replacements. However, a Crimson biome gives you the chance for a Panic Necklace (and the upgraded Sweetheart Necklace) which does not seem to have an equivalent version in the Corruption.

What items, if any, are truly mutually exclusive in function between worlds?

Even though naturally spawning ores can be mutually exclusive between worlds, an Extractinator can be used to obtain the other ores. Therefore, these ores themselves are not mutually exclusive. This only applies to pre-hardmode ores

Hardmode Ores

• Palladium vs Cobalt
• Orichalcum vs Mythril
• Titanium vs Adamantite

Palladium, Orichalcum, and Titanium items are slightly better than their Cobalt, Mythril, and Adamantite counterparts.

Crimson vs Corruption

• Crimtane items as opposed to Demonite items
• The Undertaker as opposed to the Musket
• The Crimson Rod as opposed to Vilethorn
• The Rotted Fork as opposed to The Ball o' Hurt
• The Panic Necklace as opposed to The Band of Starpower
• Vampire Knives as opposed to the Scourge of the Corruptor

The monsters in the Crimson will drop Vertebrae as opposed to the Rotten Chunks found in the Corruption. These will allow you to create the Bloody Spine which summons the Brain of Cthulhu as opposed to Worm food which summons the Eater of Worlds. Either Vertebrae and Rotten Chunks can be used to create the Mechanical Worm.