I would put my vote on BoC for a number of reasons I can soon get into, but... There's an issue with how this thread is set up. OP did not specify a location, so it's off to Central Park for them. Therefore BoC just despawns the moment the battle begins, making the match unfair. It needs to be fought in an area called the "Crimson", otherwise it just won't work. Using the bloody spine item to summon the Brain will only work if the player is in the Crimson. The other method to summon it is breaking the Crimson hearts, which (canonically) can only be found within the Crimson's caves. If the player is within the Crimson and summons it through either of these canon methods, the player must stay in the Crimson if they actually wish to defeat it; if they lure the Brain to the edge of the Crimson, the moment they step out of the Crimson and the game recognizes them to be standing in another biome, the Brain despawns.
Maybe this is the part where I give a bit of lore and context. While in terms of gameplay, the Crimson is recognized as a "biome" in that, if you're nearby enough crimson blocks, the
background and the
background music changes, and you will begin to encounter
Crimson-themed mobs. However, the real word definition of biome is "a large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra". Story wise, the Crimson doesn't seem to be a biome... It's a parasite. To summarize, it's a giant organism latched onto the planet. When you set foot here, the soil underneath your feet... It's flesh. The crimstone caves... are orifices, though the dome like entrances seems like pimples on your world map. The trees drip with blood and the grass has eyeballs attached to it. And it consumes. Like the
Corruption, it slowly spreads over your world. While they do roughly the same thing, these two demonic locations have a different context; the Corruption is a virus that slowly infects your world while the Crimson is a parasite that slowly eats your world. And the freakish enemies you encounter here? While they are able to roam around on their own and they're not connected to the ground, they're still "part" of the Crimson. All the living organisms that are consumed by the Crimson are simply part of a hive mind that serves to feed the parasitic land in which they now live. The Brain of Cthulhu seems to be the "queen" of this hive mind.
When you venture down the crimstone caves, the winding path makes the cave seem like some sort of blood vessel or tract of sorts. As you descend, you notice the strange white protrusions on the ceiling and floor. You realize they're spines or maybe other types bones. In that case, is the crimstone akin to some skeletal structure of the Crimson? When you make it to the bottom, the crimstone cave opens up into a large cavity that might be a cranium of sorts. It has several branching pathways. At the end of each one is a Crimson heart. Assuming these are the organs that support the life of the Crimson, you foolish smash some. After just three, you anger the hive mind and the Brain awakens to defend the body in which it lives.
The Brain of Cthulhu inside an underground cavity at the bottom of the crimstone caves
For a normal Terraria playthrough, for the gear you should have by the time you're ready to take on the Brain, it would be considered too difficult to flee back up the cave to the surface since it's a tight corridor where you'd have to tank the attacks to progress. However, if you do have the means to break through the crimstone (which you should if you're able to destroy the Crimson hearts), you can prepare a vertical tunnel ahead of time to lure the Brain (it is mobile) to the surface, or it can just be spawned on the surface in the first place if you use a bloody spine instead. In that case, it seems the Brain doesn't actually need to stay in the crimstone cavity, it can still survive at the surface or any location within the Crimson.
The Brain of Cthulhu above the surface of the Crimso
My point in explaining all of this is that this fight needs to be within the Crimson. While the Brain will technically be just fine anywhere within the Crimson, it seems implied that it normally resides within the cavities at the bottom of the crimstone caves, while that is where most players face it when they're finally ready to face it for the first time within their world. The fact that the Brain despawns the moment you leave the Crimson seems to imply that it cannot leave for some reason, that reason likely being that it needs to stay in the Crimson to survive. After all, it is a vital organ of the Crimson, and the Brain needs the Crimson to live (vice versa does not apply; the Crimson can continue to thrive even after you've broken all the hearts and killed the Brain several times).
All that being said, the Brain cannot fight in Central Park, New York City, unless the area is covered in enough Crimson, otherwise it will just despawn (or die) the moment the combatants are teleported there. The setting makes this unfair.
Bottom line, I cannot place my vote until OP changes the location to be anywhere in the Crimson, preferably in the crimstone caves.