Destroyers are mainly for offensive while frigates are for defensive, disregard of the size of the frigates. Some frigates have displacement larger than destroyers but their weapon configuration can still be at the level of tradtional size frigates, simply due to the role/mission requirement, but sized up for endurance, range, crew comfort and having room for future upgrades.
Yes, the mission (and respective weapons layout) determines the displacement, not the other way around.
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For the Chinese Navy, which can build the entire spectrum of surface warships for different roles, I think it's better to split it into the following missions:
1. Destroyers (Type-052D Cost ~$600 Mn?)
Long-range air defence with large, expensive AESA radars and 64+ VLS cells.
Very-high speed (30+ knots), able to keep up with aircraft carriers
Have a full ASW suite include bow sonar, TAS, VDS and 1 helicopter
Primary wartime mission is long-range air defence. Secondary wartime mission is antiship or ASW
For high-threat environments.
2. Frigates (Type-054B Cost ~$300 Mn?)
Medium-range air defence with a small rotating AESA radar and 32 VLS cells
High speed (26 knots) which is enough to keep up with everything else
Have a full ASW suite include bow sonar, TAS, VDS and 1-2 helicopters
Primary wartime mission is ASW and medium-range air defence for convoy escort.
If in a high-threat environment, operates under air cover or with accompanying destroyers
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During peacetime, the Frigates see more distant deployments.
That frees up Destroyers to remain at high-readiness and ready to surge deploy in an emergency.