Ancient Horn

Get the Basilisk moving and running through an enemy hurts it. Anything the charge connects with cannot deal contact damage back on that pass, so at speed you can plow through a pack and come out clean, though whatever survives will still hit you if it touches your hitbox afterward. The damage counts as summon damage rather than melee contact, so minion accessories raise it, and running the length of The Destroyer racks up hits faster than most weapons available at that point.

The Unicorn is faster in a straight line and goes untouchable while charging. The Basilisk reaches speed quicker, sits lower to the ground, and can charge again sooner while hitting harder. That trade favors the Basilisk anywhere with a ceiling, which is most of the underground, and favors the Unicorn on open surface runs.

Neptune's Shell turns it into a genuinely quick underwater mount. An Umbrella, a Featherfall Potion or Djinn's Curse converts a jump off any high ledge into a long glide at charge speed. And because the charge builds momentum the way sprint accessories do, mounting while already sprinting, or straight after a Shield of Cthulhu dash or a cancelled grapple, starts the charge immediately instead of making you run up to it.