The context of the two books gives an insight:
In the Psalm, the Psalmist is saying that those who follow God (The Righteous) will flourish. The Righteous delight in the LORD (vs 4-5), they Praise the LORD (vs 1-3), etc.
Isaiah on the other hand is a book of Judgement on Israel. Isaiah 57 looks at the fact that although Israel is chosen as God's people, they have chosen not to follow God (vs3-13). As such God has given His "Righteous" people over to destruction as we see Israel & Judah destroyed and taken into slavery.
The point I think Isaiah is trying to make is that although you might have been God's chosen people, you need to listen to Him and follow His commands, otherwise destruction will come and the idol's you had turned to will not be able to save you.