The Battle Cruiser is a slow but powerful military ship, armed with advanced turrets designed for long range attacks.
Its only variant is the Pyrphorian Battle Cruiser.
The Battle Cruiser is the first steam warship that can be built and it is the last word in long-range warfare. While it lacks the sheer firepower of a Ship-of-the-Line and can't hope to catch a Frigate with the wind at its back, being steam-powered immunizes the Battle Cruiser to the vagaries of the wind, allowing it to dictate the position of battle. This allows it to put its enormous range to best use--the Battle Cruiser outranges not only every other ship in the game but even shore-based Mounted Guns. Should it come down to trading blows, the Battle Cruiser has the most health of any warship and is almost completely immune to damage slowdown.
In addition, the Battle Cruiser's guns are mounted in turrets - two in front, one in the rear - meaning it can bring cannons to bear regardless of orientation. For it to use all three batteries and fully live up to its stated damage output however, it will still need to have its intended target at its flanks, where all three turrets have an unobstructed field of fire.
All this comes at a cost--the Battle Cruiser is by far the most expensive ship to build and maintain, at a whopping 850 credits of upkeep and another several thousand in the supply chains needed to construct it. A player fielding Battle Cruisers in any number is one to be reckoned with.
Battle Cruisers do not, on their own, replace sailing fleets--the three Frigates you can buy for one Battle Cruiser's cost in influence can kill it, even if it will likely kill one or two of them. However, its range is key to cracking large numbers of shore defenses, making it the tipping factor in just about any war.
The Battle Cruiser has the highest Naval Power rating of any ship in the game--its inherent rating of 70 can handle any challenge an Expedition can throw at you, leaving its capacious cargo holds and item slots for other useful tools.
Cruisers in the 1800s are warships designed and devoted to the role of long-distance independent operations, or cruises. The armored cruiser as a specifically designed warship did not evolve until the 1870s, as a derivation from early ironclads such as HMS Warrior. They were faster than line ironclads, trading armor for operational range, but at this time pure steam power was still slower than combining steam and sails. The Anno 1800 Battle Cruiser most resembles these ships. 
The battlecruiser, by that specific name, is a concept of the 1900s, rather than the 1800s. It was developed in response to the armored cruiser: a ship carrying battleship-caliber guns but sacrificing battleship armor for speed. These ships were poor combatants in a battle line (as shown at the Battle of Jutland where a number of them exploded) but were excellent at the role of hunting down armored cruisers. 
Union Update 2 (May 15, 2019):
- Damage buffed from 245 per shot to 280 per shot (official patch notes noted 275 per shot)
- Hitpoints buffed from 5000 to 6000
- Upkeep buffed from -1000 to -850.
Game Update 5 (September 10, 2019):
- Purchase price increased from 70k to 800k (official patch notes suggest it was 90k previously)
- Selling proceeds increased from 70k to 400k