Does 2 Corinthians 8:13-15 promote the notion that God desires that all congregations of His people be the same in abundance?  Is financial equality an aim of the church?

God’s primary task for the church is to save souls through the proclaiming of the gospel and help the souls within the church to grow stronger spiritually (Mark 16:15; 1 Pet. 2:9; Eph. 4:15-16).  The New Testament examples and commands which pertain to the church concerning benevolent help are a means to the end of achieving the primary task of saving and edifying souls (2 Cor. 9:8-14).

Thus, the directive to the Corinthians to ease the burden of their suffering Judean brethren was given with the goal of edifying the Judean brethren and saving the lost. 

These directives were not given with the goal of achieving financial equality among all local congregations within the body of  Christ since a) the focus of the mission of the church has always been spiritual rather than material, and b) such would be an impossibility due to the economic reality that there will also be rich people and poor people in this world (Matt. 26:11; James 2:1-7).