Not every claim is the same. You can't really compare China to Greece, China is a nuclear power, millions of soldiers, she already showed not fearing using force.
Portugal's EEZ claim for example is larger than the size of India.
Excluding small island states, the seafood consumption per capita is the highest in the world, you can literally smell it in their supermarkets, and this traditional diet is supported to a large degree by the fishing industry within their EEZ.
The proposed EEZ forms one continuous area with the mainland, something that can't be said for US, UK and French posessions.