The first scene was on the Earth. Here is an important FAQ from IMDB, where it clearly states:
There is no definite answer. It could very well be Earth in the early stages of life, possibly sometime after the extinction of the dinosaurs (the meteor which was responsible actually resulted in a mass extinction of nearly all life on the planet; the Engineers could have chosen Earth as it was a planet capable of supporting life, and maybe saw the creation of humanity as a way to "heal" the damage). However, there is no indication that it is specifically Earth. It could very well be another planet, as it is suggested that the Engineers created other life besides humans.
Another site stated supporting it was Earth:
Our Theory: What we are seeing in the beginning is the creation of Earth. The giant ship (which is different from the ring-shaped one we see later in the film, weirdly) has landed on Earth to drop off the Engineer so that he can terraform the planet and make it sustainable for life. We think he drinks the black goo to break down his own structure and spread life on Earth through his own DNA, but that doesn’t really explain his surprise while he’s disintegrating (and if the Engineers do have the same DNA as us, it’s hard to say why the Engineers had to be broken down in order to create humanity)
The Prometheus forum also states it is Earth showed in the first scene:
The engineer basically killed himself by drinking that stuff, which broke down his body and allowed his DNA to be dispersed and then (as per the film) this kick started life on Earth.
As far as the same landscape is concerned you can see there is are touches of "slight greenery" in the first scene, whereas when Prometheus was entering the planet, no such greenery could be seen! Also water was present in the first scene, whereas no signs of water was there before entering the cave in Prometheus. The planet was full of rocks, sands and all. No signs of life was there. This makes the two landscapes different. However filming was done on the Earth only. So there can be some similarities...
slight greenery in starting scene
greenery as well as water in the first scene