A first answer to this question is that both the Old & New Testaments do present the very same God. Often people believe that the Old Testament God is a violent, wrathful being whereas in the New Testament he is a God of love. This is a common misconception for God is both wrathful and loving within both the Old & New Testaments.
The fact is that the Old Testament encompasses a much larger time period where we get a fuller revelation of God. Whereas the Old Testament chronicles a lengthy history of Israel from its baby stages up until the time just before Jesus, the New Testament chronicles Jesus’s coming onto the scene as a fulfillment of God’s promises, his ministry, as well as the movements & issues of the early church. In this way if God was really involved in history then of course we are going to see more about the revealed nature of God in the Old Testament as opposed to the New Testament. This is undoubtedly a reason why people believe that there is this dichotomy between the way God is presented in the two testaments.
Sure, there are violent episodes in the Old Testament where God commands the death of wicked people including men, women, children & animals (Deu. 20:16, 17, Numbers 31:17, Joshua 6:21, 1 Samuel 15:3). However, in the New Testament God slaughters his own son on a cross for the redemption of all people. When Ananias & Sapphira lie to God in the New Testament, God strikes them dead. In the Old Testament God implores his people to turn to him and live, and that he does not wish for anyone to die (Ezekiel 18:32; also see: Isaiah 31:6, 55:7, Jeremiah 3:14, Zechariah 1:3, Job 22:23,). Likewise the Old Testament God is a God of righteousness, justice (Job 37:23) and love (Psalm 86:5); something repeated in the New Testament (1 John 4:8, Ephesians 2:4). In fact, mercy is far more apparent in the Old Testament than in the New if we were to take into account the amount of times Israel rebels against him, and how often he implores them to return.
I think that it is pretty clear that God is the same being presented in the Old & New Testaments. We simply see far more of God in the Old Testament than is presented in the New.