The Origin of Species question

"Influential" is a broad term. Politically? Culturally? The Origin of Species, and the theory of evolution, is the bedrock and foundation of the field of biology--it changed fundamentally the study of the living world. On the other hand, it somehow helped inspire subcultures that seem to have irreconcilable differences to this day. I haven't read Principia, but my understanding is that it explained the motion of the planets. In this day and age, we don't seem to have subcultures, popular books, and high-school textbooks focused on the defense or denial of Newton's theories; rather, we have thriving fields of physics that have since built on Newton's astounding work. One thing the two greats had in common, was that both Newton and Darwin were well-versed in the Bible, and began their scientific studies in biblical teachings. Ultimately, both had to rely on observations and inductive reasoning to come to their revolutionary findings.

Sadly yes.

In how far?

Newton's mechanics is perfectly relevant where it is applicable, and that is everywhere around us on earth, in the solar system, in the galaxy, and in the universe. However, anyone who reads the Principia today will have great difficulty with it, because although Newton invented calculus (along with Liebniz), he developed the Principia using geometrical methods. There is no question that the Principia had a greater impact than Darwin, because it applied to all macroscopic properties of matter, while Darwin focused on one biological process, natural selection.

Absolutely - Darwin's work has been excepted as a truth.
In terms of Newtonian Science it has laid the ground work for Einstein's Theory of relativity that redefined
our understanding of gravity.

Newton's science is for the most part is obsolete-although we will always like the "apple story".