This is basically an upside-down Ghost Ark with a huge cannon underslung beneath it. The Doomsday Ark probably got its idea from some Necron Lord or higher ups who thought that killing the primitive's tanks with their floating boats was so hilarious that it would be even better to modify said floating boats into a Necron self-propelled gun that can immolate their largest Titans. Just for the kicks.
According to our #1 Machine Molesters, Doomsday Arks are powerful enough to bring down an Adeptus Munitorum-standard M.39 “Scutum” prefabricated bunker in a single bombardment. A Doomsday Ark, when encountered, must therefore be dealt with before it can move into firing position: a single salvo can leave an entire detachment in ruins. Whatever personal eccentricities they might individually favor, all Necron Overlords hold an absolute belief in victory through overwhelming firepower. Some of the Necron‘s bitterest enemies have claimed this is simply due to the Necron’s android forms being somewhat less than impressive in swirling melee. However, the truth of the matter is that as flesh and as machine, the Necrons have ever won their wars through the unrelenting application of superior technology. As such victories are invariably won at a distance, all Necron battle codicils emphasize ranged superiority. Nowhere is this more evident in the Doomsday Ark, which is amongst the most feared of all weapons In the Necron arsenal.
On the Tabletop
Doomsday Arks deals out big steaming helpings of FUCK YOU! in the form of S10 AP-5 large blasts with 72" range when it stays still, or a S8 AP-2 blast with 36". range if it moved, which is still nothing to sneeze at. Can reliably eat MEQS, TEQ and armoured vehicles for breakfast.
It is a very good model to have on the deep end of the table, but if the enemy Deep Strikes anything dangerous too close to it, you better run away and let your troops do the clean-up. Don't let the defensive Quantum Shielding fool you, it will go down if targeted properly.
This brings us to one of the main problems of the Doomsday Ark: if it moves, it cannot benefit from the full power of the Doomsday Cannon, though even so it's still nothing to sneeze at. The other problem is that at T6 (or AV 13 in older editions), it is only moderately durable aside from the quantum shielding.
In prior editions you could team it up with a Triarch Stalker to fuck anything that you don't like; this is still possible in 9th to some extent (granting re-rolls on 1's to hit), but the Stalker doesn't synergize well with the Doomsday Ark because the Stalker likes to be close to the target while the Ark likes to be as far away as possible. That's ok though, because as long as it doesn't roll terribly the Doomsday Ark can still one-shot just about anything.
In conclusion this thing is just a massive sod off tool. Feeling sad? Well, use this to blow up the bugger who made you sad, especially if the target is a Riptide.
In 8th edition, the Doomsday Cannon is D6 shots S10 AP-5 D D6 at 72" or D6 shots S8 AP-2 D D3 at 36" if moved. Combined with 14 PV and the Quantum Shielding, the Doomsday Ark is a good support unit (it outperforms the Fire Prism against T7 to T9 vehicles).
9th Edition is here and the Ark is still competitive, although depending on what you are facing the new Canoptek Doomstalker may be a reasonable sidegrade depending on your situation.
In addition the Ark still retains hitting power at extreme range, the fly keyword, and a very solid secondary volume of fire with its array of Gauss Flayers. Whether you take it or a Doomstalker is such very much a matter of playstyle as well as which synergies you want to focus on within the Codex.