On many U.S. of A. pennies on one side is a image of the Lincoln Memorial in Washingto, D.C., a monument to a man. On the other side of the exact same coin is an image, a likeness of the man himself. The monument honors the great accomplishments of the man, but the image represents all of the man both good and bad, accomplishments and failures. Comparing Psalms 105 and Psalms 106 two things stand out. The first is that they both follow a chronology of the children of Israel being freed and led from Egypt to their promised land. The second is that they are the same account seen two very different ways. The first in Psalm 105 tells of the greatness of how God worked in, around, through, and for the children of Israel. This includes Joseph being taken to Egypt as a slave, but later rising to power, the plagues, the opening of the Red Sea, the years in the wilderness, and into the land promised to Abraham. Then Psalm 106 follows the same history with the realization of the failures in general there were by the children of Israel in most of those circumstances. Everything was from the exact same time frame and activities, but the difference was first seeing God's power and actions of love to the people, people who believed in Him, those who didn't, acting in lives of a people, a nation, and in the lived of individual people. But then the other side is presented to those to whom God's great love was extended over those centuries of time.
Then sent he Moses his servant, and Aaron whom he had chosen. They shewed among them the message of his signs, and wonders in the land of Ham.
(Then there were nine devastating signs the Lord brought upon their adversaries.)
He smote also all the first born in their land, even the beginning of all their strength. He brought them forth also with silver and gold, and there was none feeble among their tribes. Egypt was glad at their departing: for the fear of them had fallen vpon them.
Psalms 105:26-27, 36-38 GNV
We haue sinned with our fathers: we have committed iniquity, and done wickedly. Our fathers understood not thy wonders in Egypt, neither remembered they the multitude of thy mercies, but rebelled at the Sea, even at the red sea. Neuertheless he saved them for his Names sake, that he might make his power to be known.
Psalms 106:6-8 GNV
Being one of several examples that are throughout these two accounts demonstrate God's might and care for His people and how they didn't recognize it as God's working. They didn't even think of it being God's way of caring for them when the opened a mile wide path for two million people to cross through that sea in one night. Three days later they were complaining that God brought them there to die of dehydration, no water. Because of their own immediate wants, rather needs they didn't even think the God who parted the sea could provide them with the water those same two million needed to simply stay alive. Yet for His own name's sake He saved them, He loved them. How did that work in their lives?
Then believed they his words, and sang praise unto him. But incontinently they forgot his works: they waited not for his counsel, But lusted with concupiscence in the wilderness, and tempted God in the desert. Then he gave them their desire: but he sent leaness into their soul.
Psalms 106:12-15 GNV
And so looking at Psalm 105 it is all about the power and greatness of God's love alone. But Psalm 106 reveals the nature of man and still God's love and mercy.
Many a time did he deliver them, but they provoked him by their counsels: therefore they were brought down by their iniquity. Yet he saw when they were in affliction, and he heard their cry. And he remembered his covenant toward them and repented according to the multitude of his mercies,
Psalms 106:43-45 GNV
These Psalms were written in David's day twenty eight generations before Jesus came to dwell among us, yet in His day little had really changed. After the feeding of the five thousand Jesus had to get away from the crowds because they were going to force Him to become king (John 6:14, 15) and the next day on the other side of the sea in Capernaum He faces them with their completely missing the point of the feeding of the five thousand (John 22:25-35). Then later at the raising of Lazarus (John 11) many believed on Him, but others went to the Jewish elders not believing (Compare with Luke 16).
But this continues in our lives today. We see the mighty works of God, the love of God in those works and even the best often say, Lord, I believe, but help my unbelief. That other side of the coin says yes, throughout the Old Testament, and New Testament, and time and again since then until today there are still those like Joshua and Caleb, Eliezer, Daniel, and many more who didn't go along with the crowd, but still have said,
Psalms 106:47-48 GNV
Save us, O Lord our God, and gather us from among the heathen, that we may praise thine holy Name, and glory in thy praise. Blessed be the Lord God of Israel for ever and ever, and let all the people say, So be it. Praise ye the Lord.