The Egg Carrier 2 was the second Egg Carrier that Doctor Eggman had built. It appeared only once briefly in Sonic Adventure; he had tried to use it against Chaos in case he rebelled and refused to obey orders. Consequently, it was destroyed while attacking Perfect Chaos. The same thing happened in the Sonic X adaption.
In Sonic Adventure, and it's enhanced port Sonic Adventure DX Directors Cut, the Egg Carrier 2 was built in case a rebellion from one of his subsidiaries. When Chaos retaliated against his former master, it was launched by Eggman to combat Perfect Chaos, though it never lasted more than a minute, as Chaos's powers seemed to surpass that of the new war ship. Subsequently, Chaos managed to obliterate the carrier with a single, powerful blast, destroying the Egg Carrier 2.
In the Sonic X adaption of the game, the Egg Carrier 2 was launched to defeat Chaos, much to Sonic's irritation. While at first seemingly impressive, Chaos managed to deflect the attacks in a similar fashion to the helicopters, and blew the war ship out of the skies, sending Eggman and his two servants flying.
The Egg Carrier 2 seemed to have no difference to the original carrier, despite having a large numcer 2 painted on it's flank. Possesing the exact same firepower and prowess, it was meant to be a back-up plan in case of any rebellion, such as Chaos.