The behaviour and attributes of God is consistent between Christianity, Judaism and Islam in the Old Testament.
Christianity branches off cos it has a new testament where we're forced to believe that either God got replaced by a calmer God somewhere between testaments, or he really mellowed with age and stopped smiting people/wiping out their first-borns and started talking about loving one another and treating others as you would wish to be treated.
And then you also happen to know that Christians believe that Jesus is God, and he is also a spirit a father. Which both Islam and Judaism deny, and then at the same time you claim in the first quotation i made that the attributes of God is consistent in the three faiths. So no they are quite different, which you also say in the second quote. And the stories in the bible are different in the Quran, where god acts differently.
And when you say "they all believe in the God of Abraham" that is incorrect. The Christians believe in a God that is defined by the trinity and the Jews believe in a God that is not. Now there's only one God speaking to Abraham in the bible, and the attributes of God differ between these two religions. The Muslims believe Abrahams God was their God. In fact Muslims believe that every prophet in the bible was a Muslim and spread Islam, but the religion was corrupted with time into other religions such as Judaism and Christianity where polytheism and kufr was introduced, and then Muhammed was sent as the final prophet to reestablish the religion. So they believe that they used to believe in Allah, but deviated and are praying to idols, and other gods or deny the attributes of God. Even in the hadith the Jews mock the Muslim God in debates with Muhammed, where they call Islam's God poor because its an obligation for Muslims to pay zakat (
http://www.qtafsir.com/index.php?option=com_content&task=view&id=759&Itemid=60 Too much to quote read this site if you care).
And:
http://islamqa.info/en/67626The Jews and Christians are both kaafirs and mushrikeen. They are kaafirs because they deny the truth and reject it. And they are mushrikeen because they worship someone other than Allaah.
Anyways it's quite subjective like I said, if your assumption is that they believe in the same God, because the religions share same roots then so be it. I don't think they should be considered the same God because if you compare the three they are different. But the respective followers of each religion believe it's their God in the stories.