To me, this has always been a bit of an interesting question because while I think there are certain common threads that link the disparate elements of the Enlightenment, I also think that there's a distinct sense that the movement encompasses a fairly large time period and a lot of different cultures, and increasingly I'm wondering if it's helpful or even possible to just talk of "The Enlightenment" (i.e. just how much common ground is there between, for example, the French Enlightenment in the 17th century and the Scottish Enlightenment in the 18th century).
To me it's a very interesting question, and I was wondering if any of the experts on here might be able to shed some light on it.
here's my opinion as someone who both uses the notion of "the enlightenment" but at the same time loves to challenge broad generalizations:
First of all, as a general principle, we can take a microscopic look at almost any large social phenomenon and emphasize the diversity and difference between elements of that phenomenon. this approach has its role, particularly in helping to correct broad assumptions that are restrictive and prevent deeper understandings of the causes of certain events.
Broad characterizations/generalizations, on the other hand, are useful for A) sharpening and expanding our broad vision of history and culture, B) helping people who focus on other areas see commonalities which they might not have perceived with only microscopic examples, and C) helping generate theories that can later be used to investigate micro-phenomena.
So, in the end, it depends on your perspective of what your looking at and why you're looking.
I can give you some examples of how I might use both perspectives. I do some work on the relationship between Islam and the West. There has been some research on the influence of Muslim/Arabic scientists and philosophers on 17th and 18th c Western Scientists and philosophers. Generally it seems that by the late 17th c--around the beginning of the enlightenment, some would say--that influence began to seriously wane, and it hadn't been all that prominent in the past anyway. If one were to take a broad view of the enlightenment, it would therefore be hard to argue for a significant--if any--influence from Muslim/arabic writers. However, if you took a microscopic view, you can see different, if subtle trends in influence emerge in different regions and among different types of thinkers (especially british ones). Only by emphasizing difference and diversity in the enlightenment, then, can the influence be fully appreciated.
at the same time, however, if you wanted to compare the broad intellectual development of the west with that of Islamdom, it may be helpful to observe general trends. The presence of the european enlightenment definitely comes into relief, and you can start to develop general theories with this knowledge. Plus, by taking this multi-civilizational approach, one can gain a better view of world intellectual history.
Of course, if you only have broad generalizations, your theories are going to be broad and crude, and can lead to stereotypes. These theories therefore should be constantly tested on microscopic levels. In some cases, theories can help you learn more things that you might not have otherwise because you had no other reason to pursue that line of investigation. So, one of my favorite examples of this for Islam-Western Englightenment things is the discovery of the likely significant influence of an Islamic philosophical treatise on Locke's thinking. There had been growing awareness of early modern Western interest in Muslim/Arabic writing and after a few essays and books were published--some of which offered general theories on the topic--one scholar investigated the possibility of Locke being influenced, and made a pretty convincing case. However, at the same time, her investigation shed light on just how rare something like that would have been. Overall, then, it's best to be able to have both broad and microscopic perspectives.
The first book on the enlightenment i read was peter gay's "the enlightenment"--it is 2 volumes and definitely presents both the broad and the microscopic, and specifically addresses the issue you're asking. Although i think it's around 50 years old now, id still recommend it.