This is a difficult question to answer, because theologians are constantly arguing with each other about views on heaven and hell. So, there is little consensus even among theologians of each religion. In light of this, I will limit myself to general points.
From a traditional point of view, both Christianity and Islam believe in heaven and hell. Christianity says that heaven is a place where there is no sorrow, no pain and blessedness. There will be a new heaven and a new earth and God will be there and this will be the cause of joy. At times, heaven is portrayed as a wedding feast and at other time heaven is portrayed as paradise or a renovated garden of fellowship.
In Islam heaven or paradise (firdaws) is a place of physical and spiritual pleasure, mansions, feasting and interestingly virgin companions. From this description, it is similar to Christianity apart from the virgin companions.
Hell within Christianity is described as outer darkness, the place of gnashing of teeth, and a fiery lake. These are some of the most common descriptions. However, it must be stated that hell is not mentioned too much in Bible, even though it is definitely there.
Hell, or Jahannam in Islam is mentioned frequently and it is seen as a place of fire and various levels. The deepest level has a boiling cauldron and it is reserved for the worst transgressors.
The difference between Christianity and Islam when it comes to hell is chiefly the various levels that Islam has. In the end, what really differs between Christianity and Islam is how one gets into heaven and hell.