Well, let me make a run at it. Probably shall serve as an explanation to why I don't really see the need for any excessive capability for a big navy frigate, too. 2nd line navies that are compensating for their lack in something (Major European navies, incl. Russian one, Japanese navy) have a big lure in big superior frigates - but for big 2 it's ultimately either a worse destroyer or a ship that took a place from a more reasonable frigate and a fleet destroyer.
Cruiser: blue water ship, capable of fully and simultaneously supporting and fulfilling various tasks of air-sea fleet action (including counter space), while simultaneously supporting heavy anti-shipping/land strike potential. Flagship and key node. Core combatant of surface battle fleet.
Task: flagship, local air/sea superiority, anti-ship and land strike.
Example: 055 in our case, though slightly borderline with a big destroyer (core node, if it even needs to be, probably shall aim at some sort of ability to take hits and remain combat-capable; subject to discussion).
Destroyer: universal blue water combat ship, intent on fully participating in air-sea fleet action at its normal combat ranges (hundreds of miles). Line combatant of the surface battle fleet.
Task: local air/sea superiority, fleet action.
Example: 052D
Frigate: green or blue water ship, intended primarily on either fulfilling its own missions under the umbrella of the battle fleet or friendly coast, or fulfilling its own separate missions wherever mission doesn't call for the employment of full battle fleet formations.
Task: escort, multipurpose combatant; trade protection.
As a ship that can be dedicated to fulfilling various submissions (local air defense unit, strike, colonial cruiser - specialized versions are highly likely for navies that can't afford destroyer-centric ecosystem as their main combat strength) - specifics may vary, but the general outlook as above.
Example: 054A, B
Corvette: green/brown water ship, intended at fulfilling specific local missions under the umbrella of the friendly coast.
Task: coastal escort/sea control, trade protection.
As a ship that can be dedicated to fulfilling various submissions (local air defense unit, strike, colonial sloop - specialized versions are highly likely for small navies there littoral specifics are forced onto them) - specifics may vary, but the general outlook as above.
Example: 056A
Cruiser: blue water ship, capable of fully and simultaneously supporting and fulfilling various tasks of air-sea fleet action (including counter space), while simultaneously supporting heavy anti-shipping/land strike potential. Flagship and key node. Core combatant of surface battle fleet.
Task: flagship, local air/sea superiority, anti-ship and land strike.
Example: 055 in our case, though slightly borderline with a big destroyer (core node, if it even needs to be, probably shall aim at some sort of ability to take hits and remain combat-capable; subject to discussion).
Destroyer: universal blue water combat ship, intent on fully participating in air-sea fleet action at its normal combat ranges (hundreds of miles). Line combatant of the surface battle fleet.
Task: local air/sea superiority, fleet action.
Example: 052D
Frigate: green or blue water ship, intended primarily on either fulfilling its own missions under the umbrella of the battle fleet or friendly coast, or fulfilling its own separate missions wherever mission doesn't call for the employment of full battle fleet formations.
Task: escort, multipurpose combatant; trade protection.
As a ship that can be dedicated to fulfilling various submissions (local air defense unit, strike, colonial cruiser - specialized versions are highly likely for navies that can't afford destroyer-centric ecosystem as their main combat strength) - specifics may vary, but the general outlook as above.
Example: 054A, B
Corvette: green/brown water ship, intended at fulfilling specific local missions under the umbrella of the friendly coast.
Task: coastal escort/sea control, trade protection.
As a ship that can be dedicated to fulfilling various submissions (local air defense unit, strike, colonial sloop - specialized versions are highly likely for small navies there littoral specifics are forced onto them) - specifics may vary, but the general outlook as above.
Example: 056A