Many differences between the two can be found, even when measured by stylometry. At the first sight, the written texts are more "gramatical", have longer and more complicated sentences, more diverse vocabulary etc. than the word by word transcribed texts. Especially dialogues. Interesting is that the early Arabic literature is claimed to have "oral" character, i.e. that it is stylistically simmilar to the spoken language.
Of course, the difference between the MSA and the dialects is enormous. And the difference between the historical written Arabic and historical dialects is possibly also enormous (but this field is quite unexplored and the question is whether it can be explored). Whait I meant is that the early Arabic texts have some stylistic features of oral language, e.g. it uses a lot of parataxis instead of hypotaxis. But I have never seen any corpus based study that would test this hypothesis properly, it is only a traditional claim...
When we transcribe an oral corpus, it is still an oral corpus. What we do by adding the transcription is to include metadata about the intonation, pauses and other issues of orality or other (e.g. who is speaking), but the language originally produced and collected in the corpus remains exactly the same, and hence it is still oral.
When defining a corpus either as a written corpus or as an oral one, we are only describing the original mode of production of the language contained in it.