Justice or Righteousness

So recently I've been trying to wrap my head around a couple of things one that I'll be leaving in little over a week "ERMAHGERD"

 and the other "issue" is more a theological/exegesis debate that revolves around the translation of dikaiosynē. The Greek word can be translated into either ‘righteousness’ or ‘justice’. 

I have been thinking – when many hear ‘righteousness’ they automatically assume a personal, private holiness and piety, and Justice gives a connotation of how we relate to others as well.

For example, reread these passages with justice rather than how we hear them normally (translated as righteousness):

Matthew 5:6 – Blessed are those who hunger and thirst for justice, for they will be filled.

Matthew 6:33 – But seek first for the kingdom of God and his justice, and all these things will be given to you as well.

They have a different ring to them, don’t they? Does this change the passages? Or is it still the same way? Or do you believe that Jesus was indeed talking about personal piety and not larger justice issues?