Usually when something is ground it can lose some properties, e.g. a lot of seeds can lose their oil.
Does fresh chilli contain anything such as oils or anything else which a store bought powder may not have due to the processing?
The main property that is different is that fresh chili peppers contain water. That means a significant difference in the kinds of flavors that are perceived when you consume them. Probably, most specifically, that fresh, "green" flavor and aroma that you perceive when using fresh. There are probably volatile aromatic properties that lost during dehydration. You can confirm and choose the variety of pepper when using fresh. Ground, dried peppers are more difficult to identify, unless the variety is indicated on the package. It also looks like dehydration decreases ascorbic acid and carotenoids, which would impact the nutritional contents, and likely, how the flavor is perceived.
Personally, I think of them as two different products.