Ada Lovelace was the first to realise that the analytical engine would perform arbitrary tasks and wrote programs for those arbitrary task, beyond computational operations. Of course Babbage who designed the hardware had some idea of what programs it could run and presented examples, but he did not have the forethought to go beyond as Lovelace is quoted in your articles, "an original understanding of where the power and potential of computers lay."
There has always been a controversy of how much of Lovelace's work is hers and how much is Babbage's in the Menabrea papers, and I don't think Babbage writing a few simple programs settles this controversy one way or another. Lovelace had unique and original insights that should not be downplayed.
