Muslims believe Allah and Jehovah are One
From the perspective of the Muslim, when they are praying to Allah, they believe they are praying to the same person whom Christians would call God.
And do not dispute with the followers of the Book except by what is best, except those of them who act unjustly, and say: We believe in that which has been revealed to us and revealed to you, and our God and your God is One, and to Him do we submit. [Quran 29:46]
And there are, certainly, among the people of the Scripture (Jews and Christians), those who believe in God and in that which has been revealed to you, and in that which has been revealed to them, humbling themselves before God. They do not sell the Verses of God for a little price, for them is a reward with their Lord. Surely, God is Swift in account. '(3:199)'
Verily! Those who believe and those who are Jews and Christians, and Sabians, whoever believes in God and the Last Day and do righteous good deeds shall have their reward with their Lord, on them shall be no fear, nor shall they grieve . [Quran 2:62]
Add to the concept of "the people of the Book," the fact that the most important thing for Muslims is the fact that God is one (as you said), and the fact that Muslims recognize the Old Testament as Scripture, albeit a corrupted one, and it is clearly fair to suggest that Muslims believe that Jehovah and Allah are the same person.
Christians Have a radically different understanding of God's character
Unlike Allah, however, Christians see God as far more full of mercy, compassion, and grace. Additionally, while we believe in God's perfection, glory, and holiness, fundamentally we disagree about God's willingness to pursue his people. Much like "the Return of Martin Guerre," there is some question as how radically different the character of an individual can still be and have it actually be "the same person"
Christians, for example, believe that God had a son. Muslims say that Allah cannot "beget". Muslims say that Allah cannot become a man. In short, while Allah could be reconciled with God the Father, there is no way to reconcile Allah with God the Son, in the form of Jesus the Christ.
Indeed, Muslims are explicit in denying the deity of Christ. They say:
They (Christians) allege: The Gracious One has taken unto Himself a son. Assuredly, you have uttered a monstrous thing! The heavens might well burst thereat, and the earth cleave asunder, and the mountains fall down in pieces, because they ascribe a son to the Gracious One; whereas it becomes not the Gracious One to take unto Himself a son. There is no one in the heavens and the earth but he shall come to the Gracious One as a bondman…. … So We have made the Quran easy in thy tongue that thou mayest convey glad tidings to the righteous, and warn thereby a contentious people. How many a generation have We destroyed before them! Canst thou perceive a single one of them, or hear even a whisper of them? (Surah 19:88-99)
Furthermore, the concept of Trinity is anathema, because it violates the supreme confession of faith, both for Jews "Hear O Israel, the Lord your God is One" and the "oneness" of God that is demand is the statement "There is one God, Allah, and Mohammed is his prophet."
Biblical Understanding of Other Gods
While Muslims think they are praying the same God, Christians would disagree. Their understanding of the nature, composition, and character of God is so different, that we do not recognize their understanding to be anything close to our conception. It is as god based not on revelation that Christians accept, but rather is a man-made revelation.* It would be no different than a Christian's response to any of the gods to which Hindus pray - they are no gods at all.
Throughout the Old Testament, prophets of "the One True God," regularly derided idols as "man made gods, capable of neither sight nor hearing." They were not true gods at all.
In the New Testament, (in Acts 19), there was even a riot in Ephesus - the New York City of its day, when Paul came to down. Note the objection of the pagans, when it says:
A silversmith named Demetrius, who made silver shrines of Artemis, brought in a lot of business for the craftsmen there. 25 He called them together, along with the workers in related trades, and said: “You know, my friends, that we receive a good income from this business. 26 And you see and hear how this fellow Paul has convinced and led astray large numbers of people here in Ephesus and in practically the whole province of Asia. He says that gods made by human hands are no gods at all. 27 There is danger not only that our trade will lose its good name, but also that the temple of the great goddess Artemis will be discredited; and the goddess herself, who is worshiped throughout the province of Asia and the world, will be robbed of her divine majesty
Note that Paul himself, while clearly not recognizing the divinity of idols, is not himself calling for an intolerant public response - rather he for himself denies the divinity of other gods. He was not being disrespectful, just not accepting divinity. (Indeed, just two chapters earlier, at Mars Hill, Paul openly praised the Greeks for their religiousity in their 'Altar to the Unknown god,' and used that to bring them to a "right knowledge.")
A side note about revelation
*Yes, Muslims believe that Gabriel revealed the nature of God to Mohammed. Likewise Mormons believe that Moroni revealed the nature of God to Joseph Smith. In both cases, Chalcedonian / Nicene Christians reject the revelation given because in general consensus the alterations to the nature of the pre-established God is so different as to make many not accept it. Christianity is organic in its understanding of who God is, but it is also not uncritical of any revelation. Christians are in fact exhorted in 1 John 4 to "test every Spirit", for as it says:
Dear friends, do not believe every spirit, but test the spirits to see whether they are from God, because many false prophets have gone out into the world.his is how you can recognize the Spirit of God: Every spirit that acknowledges that Jesus Christ has come in the flesh is from God, but every spirit that does not acknowledge Jesus is not from God. This is the spirit of the antichrist, which you have heard is coming and even now is already in the world.
Nicene Christians dismiss any understanding of God that does not accept that Jesus is not God. Since Muslims reject this, Christians reject them.
Prior to the incarnation (e.g. the OT Jews), there was no incarnated Jesus, and hence this was not a valid test. In the OT, the test was whether or not a prophet was backed up by Jehovah's power (hence Elijah vs. the prophets of Baal in 1 Kings 18 and other miracles). As Hebrews 1 says:
1 In the past God spoke to our ancestors through the prophets at many times and in various ways, 2 but in these last days he has spoken to us by his Son, whom he appointed heir of all things, and through whom also he made the universe.
But, now that he has come, it is for Christians, a definitive test.
Christians would thus say, the God to which they pray is not the same God they know, and as such are praying merely to a god made in their image, rather than the other way around.