Do SQL Server or MYSQL contain JSON supporting functions?
SQL Server 2016 will support JSON strings.

Currently with the CTP2 version you can only export a table to JSON string.
But with the release of CTP3 version you can also read and store JSON string in SQL Server tables.

You can check all about how JSON will work with SQL Server on my blog. SQL Server will store JSON in NVARCHAR datatype columns only, unlike XML datatype for XML data.

Edit: With CTP 3.x you can create a Table with NVARCHAR(max) data type column to store JSON text, but make sure to add a CHECK constraint to validate the JSON, like:

CREATE TABLE CustomerOrder (
    BusinessEntityID INT, 
    FirstName NVARCHAR(50), 
    MiddleName NVARCHAR(50), 
    LastName NVARCHAR(50), 
    EmailPromotion INT,

    OrderDetailsJSON NVARCHAR(MAX) -- normal column with NVARCHAR datatype
        CHECK ( IsJSON ( OrderDetailsJSON ) = 1 ) -- CHECK Constraint to validate JSON string
)


The official SQL Server team blog also has a series of articles on this topic.