There will be many different responses to this question. In the end, sorting through them might be a challenge in its own right. One of the primary differences between both religions is simply that: Religion. For Muslims, their religion is Islam, a monotheistic religion that is quite direct in the relationship between the devotee and the divine force. For Hindus, the religion of Hinduism is quite a different experience in that it is polytheistic and the path to the divine manifests itself in many different ways. Such a fundamental difference reveals divergence in many points of daily life and the belief of human consciousness. This can even extend to the afterlife, where there is a distinct judgment in Islam of the "righteous" and "sinful" life whereas Hinduism stresses the belief of reincarnation in accordance to the deeds one has done in their life. From a geopolitical point of view in the Indian subcontinent, Hindus and Muslims were fairly heterogeneously mixed with one another until the Partition in 1947, where lines were drawn between what was considered to be the predominantly Muslim Pakistan and Bangladesh, with the predominantly Hindu India in the middle. Such division and boundary establishment has added controversy to the area of Jammu- Kashmir, in terms of whether it should be a part of India or Pakistan.
In my opinion, there is one difference between these two religions that dwarfs all others. That is the fact that Islam is perhaps the most aggressively monotheistic religion in the world (except for, perhaps, Judaism). By contrast, Hinduism is definitely not monotheistic. (You can argue that it has one supreme god, but it is okay with the idea of many different deities of some sort).
A second, related, difference is that Hinduism is quite happy to have images of its gods. By contrast, Muslims are very against anything that might seem to be idolatry.