Battleships are pretty well protected. A virtue of their armor protection not forseen during their development was that their internal side armor belt is better suited against missiles with shaped-charge warheads than the conventional, external side belts. The reason why the internal belt was adopted was because its angle was too steep for ship that had to be narrow enough to pass through the Panama Canal. The angle was stepp because inclining it increases the effective thickness without actually having thicker plates, thus saving weight, which was an important consideration in the design, as the Iowas were meant to be very fast.
Whe a missile hits the side, the blast must penetrate 1.5" of STS armor plate on the outside of the hull. Then it has to go through another 1.5" plate angled at 15 degrees after a few feet of space, and after going through more space, it must go through a 12.1" Class A (face hardened) armor belt backed by .825" STS plate angled at 19 degrees, which increases the effective thickness to around 17.5". After penetrating the belt, the blast would go into a compartment whose deck is STS plate, the roof is Class B armor plate and STS plate, and the bulkheads are 1" STS plate, which is designed to contain blast and shrapnel damage from penetrating shells. Once it goes through this, it is then free to damage the insides of the ship. A hit through the deck would have to penetrate 1.5" of STS plate, and after going through some space (between the main and second decks), it would have to penetrate 4.75" of Class B Armor (thicker over the steering gear and main machinery) combined with 1.25" of STS, and then after some more space, it would have to go throuh a .625" STS splinter deck, and the third deck would be next, which also is made of STS plate.
The main threat from missile attacks is not the destruction of the ship, but damage to electronics and exposed systems, which can inhiit the ship's ability to fight. One advantage that the battleships have in this regard is systems redundancy, as well as blast-hardened electronics, which must be made such due to the blast from the 16" guns. The ship has 4 secondary battery directors, 3 main battery directors (one housed in the armored conning tower's upper level), and also has surface and 2D air search radars. The turrets also have their own optical fire control components and radar velocimeters, as well as fire control computers. The secondary battery has optical fire control instruments as well. If there is loss of power, the secondary battery can be operated manually, as can the directors, which can use only optics for fire control, and do so effectively. This all helps to keep the ship in the fight, despite taking on considerable damage. There are also to CICs, one behind the armored conning tower, and another deep in the ship in the plotting rooms.
Against side-hitting torpedoes and mines, there is considerable protection. It was hypothesized that the side-defense system would have to be hit by 5 21" torpedoes striking simultaneously at certain intervals on one side of the ship to put it in jeopardy, although torpedo attack can result in a mission kill, depending upon the extent of the damage (the North Carolina, with an inferior system, was able to speed up after being hit by sub torpedoes and continue to operate, although she eventually had to return for repairs). There are 5 torpedo bulkeads and empty and liquid-loaded tanks and a holding bulkhead which the torpedo has to have its blast go through. One of the torpedo bulkheads is the armor belt. A weak point is where the No.! turret is, as the fine lines cause the system to be thin at that point. Against underbottom attack, the ship is more vulnerable, although it is protected as best as a warship can be. Like carriers, it is fitted with a tripple bottom, with one set of tanks being liquid loaded to aid in absorbption of the blast. Something which has never been tested is whether the ship would have a strong enough structure to stay intact if the keel were broken; noteworthy is that fact that the Class B Armor is considered to significantly strengthen the ship in this regard, although how much in this scenario is unknown.
An Iowa-class battleship is a formidable weapons platform. It's 16" guns can wreak havoc on land and surface targets, and since the modernizations, the guns are more versatile due to more shell types being available, such as DPICMs, special airburst shells (including one meant to defeat massed torpedo plane, and in mordern times, missile attacks), and other projectile types. Highly developed and near entering service was a 13.65" extended-range projectile which extended the range to over 35nm and could, if necesary, be fitted with a guidance system, although under normal conditions, it would not be so fitted. DARPA had also been developing an 11" rocket-assisted extended range shell with a 100nm range and which would come standard with guidance packages. Still being developed at China Lake are scramjet projectiles which can achieve an even greater range with short flight times.
An advantage the battleship has in shore bombardment/fire support missions is that in a period oftime it can put out more ordnance than a carrier, and do so continuously in all weather, something that carrier aircraft cannot do. It can also do so at reduced cost, and with at least as good accuracy. (Against surface targets, using only optical fire control, a battleship in an exercise was able to outscore naval aviators). The AP shells can also penetrate up to 36 feet of reinforced concrete, depending upon the range, something which bombs that can be fitted on naval aircraft cannot do.The extended range projectiles would have significantly improved this on the whole. Also, there is no risk of pilots being lost during NGFS missions, and the shells cannot be shot down. They can also provvide missiles to anti-ship and land attack missions. The planned 1990s modernization would have seen the Iowas have their Tomahawk ABLs removed and replaced with 96 vertical launch cells in four armored VLS launchers; Sea Sparrow launchers would have been fitted seperately, but a modernization using current technology would likely substitiute vertically-luanched ESSMs in quad-packs, to give the ship a moder air defense system.
The ships are also very fast (with an emergency speed of 35.4 knots, faster than any carrier currently in service, and full speed at over 33 knots), and also, when moving at higher speeds on the open ocean, highly manoeuverable. They also can be used as flagships. The battleship really does bring alot to naval surface warfare. What its main drawback is is that it is manpower intensive (although not nearly as much as a carrier, which is over 4 times as manpower intensive). The charge that it is also expensive to operate is largely unfounded, as its annual O&M costs are 1/10 those of a carrier, and not significantly more than a modern destroyer or cruiser.