Nuclear cruiser is kinda oversized for anti-piracy operation.
I guess the USA will have to send an aircraft carrier group to keep the balance
well, in actual fact an aircraft carrier is the better choice - why?
well, at the moment the combined anti-piracy fleets comprise over 60 vessels, and the various task force commanders have indicated that they cannot cover the spectrum and entire area of likely operations - in fact the 60 vessels can cover only 20% of the potential likely pirate effected region.
I can tell you that various navies have persistently stated that a medium aircraft carrier is a better choice - because it provides sea basing capability, and because it then means that the area of ops will be covered faster and more efficiently by organic air.
every major interception to date has resulted in organic air from a destroyer or frigate being advanced ahead to interdict and intercept. A carrier would/could provide far more coherent autonomous CAP/GTMI capabilities - and as such could vector assets much faster than any surface vessel.
the best assets in fact in the region are subs (ISR and port monitoring), multi-rotor supporting skimmers (eg larger cruisers or big destroyers because they have air redundancy) and fixed wing ASW assets like the Orions (because they have a huge IR sensing footprint) IR on water? The Orions excel at this and have since 1991.
Apart from these, what are the next best assets? well, at fleet level it would be aerostats - they'd then have "permanent" OTHR capability and at a very efficient cost base.
So, in short, in real terms, depending on what and how many rotors are attached to the russian cruiser, depending on its area of op, depending on the local commanders ROE's - its a far more useful asset than a single rotor equiped frigate or destroyer.
A carrier would be better - or a converted container ship, or an asset like HMAS Manoora and/or HMAS Kanimbla.
One of the experiences out of the Gulf was that the Manoora and Kanimbla were considered by far to be the most effective task force commanding ships on gulf watch - they had multiple rotors, could deploy specforces at will, had refreshed VBSS experienced teams available, and had the command centre to co-ordinate all other navies assets in theatre.
Cruisers provide that to a lesser degree, carriers (medium esp) provide it better. larger carriers are for major and probably theatre area violent prosecution, so would be overkill. BUT beggars not being choosers would rather have a large carrier for overwatch than no carrier at all.
This is not a pecker competition for who's ship is bigger - its what assets are relevant and available that counts.