That depends on weather the measure is of concept, lineage, or attribute.
First of all, as mentioned, Allah is Arabic for God and Bibles written in Arabic would likely use Allah for God or YHWH. So Allah is just God in another tongue. It's like choosing to call God YHWH, Adonai, Hashem, Shaddai or simply God.
So the question is somewhat redundant, now as for a very generalized comparison of Gods attributes by Most Christians and Muslims....
Comparison by concept: An, all-knowing, all-powerful enity known as the One, or "highest power"... The Holly of Hollies... Both Muslims and Christians ascribe these traits to their God as do many other cultures. The Wiccan term for example is Dryghten. (and this word was used in some old-English Bibles) The Egyptians call it the Kneph among other terms. Taoists see it as the Tao (though would dare not define it) and so on. You can take two stances on this. You can either say all those other guys have the wrong deity/concept or you can say that the underlying message- Unity, applies and that all of these terms are different cultural understandings of the same thing. Most divine attributes cannot exist without a condition of unity.
Lineage: This one is easy, both groups serve the God of Abraham.... they trace their deity to the same source/deity. It is the same God
By Attribute: We already went over conceptual attributes. The question presented here is - Is the character of Allah in alignment with the character of YHWH? That is... is the Islamic depiction of Allah symetrical with that of YHWH? If they act differently that indicates different morals/personality traits. This is a sleep slope though when you figure in interpretation and the views at the time the documents were written. Certain cultural influences aside I believe they can be said to be the same even here.
The short technical answer is yes.... they are the same. However just as the Greeks and Romans may have had slight differences about Zues/Jupiter and Christianity itself differences by denomination you are going to find differences between Muslim and Christian notions.
At the end of the day, you're going to have to ask yourself what you think and what makes sense to you. That may not seem very comforting but allot of this depends on interpretation and perception and in the end you have make a decision based on what you know and what your intuition is telling you. There might be a reason it can't simply be figured out at the moment until one understands the question on a multi-dimensional level. This is what people of my faith call one of the mysteries.
But I leave you with this. The name that can be named is not the true name. Nor does the true name invalidate any name. For names are formed out of relationship and God is transcendent, One.
God is not two faced, nor does He represent a different self to different people. People on the other hand perceive God differently, some just not rightly because of fellow men's and their ideologies are wrong for personal gain.
Having different parts of yourself is not two-faced. That is such a derogatory term. Our society looks at things like MPD as a disease and it is, but only when it is truly a "disorder". Many of has have multiple sides of our selves yet go our whole life not realizing it. People thing that if that's the case that you are fractured or torn and not whole. Its rather the opposite though, as you cant be whole while denying parts of yourself.
Of course he does, that's the nature of relationship.... You arent the same person to your mom as you are to your co-worker or your wife/husband/ect.
God doesn't stop being God but often a different aspect of God is projected. This is what Jewish mysticism teaches. the perception helps give God an identity in which one forms a relationship with him/her/it. It's a two way molding. Also, remember, if God showed his/her full glory it could not be comprehended and in various texts is said to be so overwhelming that the physical body couldn't withstand it.... Either one of those statements implies that God must operate on our level of communication in order to commune with us.
Jesus said that he had not come to show us who he was but who we are, and how to live. Unless you are of the Unitarian sort or otherwise don't see Jesus as God... that right there is an example of God choosing a different form than he did to Moses or Enoch.
And again, in Jewish mysticism the different emanations and forms (yes forms) of God take on different visualizations.
Lastly, to be fair - even if we assume only one vision is correct and all the others are rooted in falsehood... it would be impossible to objectively say which is true and which isn't. Likewise subjectivity tends to favor them all.
And it still doesn't address the example I gave, which is a better example of your argument given he used the bible, not another 'holy' book
