Interestingly, there has never been much agreement on this issue.
I'd agree that "Alllah" was the same monotheistic g-d that was worshipped by Jews. as pointed out above the religions fought (among a million other things) over who was the blessed child ishmael or jacob.
I think in light of the common father of both religions, Abraham the arab and jewish g-d are similar, if not the same.
However, Christianity does throw a wrench into things because on the one hand, Christianity is monotheistic, but on the other there are 3 g-ds, not one.
At times it would appear that Christian G-d is three distinct beings and so different. However, the old testament/torah discusses angels which many ancient scholars believed were nothing more than extensions of g-d, although not exactly g-d himself (or herself for you progressive thinkers), so its not really clear that christianity invented the idea that g-d could splinter although basically is one being. ( A loose analogy to the Christian g-d is a football team that team consists of three different parts, offense, defense, and special teams--all diferent but all part of the same team).
Bottom line is that whether or not g-d is the same, the members of these religions behave very differently.