The answer to this depends in large part on how we define “minority groups” for the purposes of this question. If we look only at ethnic/racial minorities, we will find that religious experiences are largely similar to those of the white majority. However, if we look at religious minorities, we can find very different religious experiences. In addition, as we answer this question we must be aware that any discussion of minority or white religious experiences will have to generalize because there are many varieties of religious experience within almost every ethnic group in the US.
If we are talking about ethnic minorities, we have to say that most of these groups have religious experiences that are similar to whites. That is, members of those minority groups who belong to churches have religious experiences in church and in church functions. (It is fair to say that the percentage of many ethnic minorities that attends church is greater than the percentage of whites that does so.) In many cases, the nature of the church experience is somewhat different because many minority churches are more charismatic and emotional in their worship than many white churches. However, this is just a generalization as there are whites who worship in evangelical churches whose worship is less staid than the worship in mainline churches. The point is, however, that the “typical” racial minority churchgoer has religious experiences in their church and with church groups, just as is true of the “typical” white churchgoer.
If we are talking about religious minorities, the story is much different. Here, there truly is a diversity of religious experience. Let us look at two examples in which religious minorities’ experiences are different. First, there are minority churches that demand that their members act in ways that are very different from those of mainstream society. For example, Seventh-Day Adventists (many of whom are non-white) observe the Sabbath very strictly and do so on Saturday rather than on Sunday. They also typically follow dietary rules that make them different. As another example, members of the LDS Church (Mormons) tend to go on missions when they are young, which is a religious experience not shared by people of most religions. Second, there are minority religious groups that withdraw physically and behaviorally from society. The most notable of these groups is the Amish who forego the use of much modern technology and who live apart from mainstream society.
Thus, the answer to this question is very different depending on whether we look at ethnic minorities or religious minorities.