The Einstein poster’s a nice touch. A reminder that Peter Parker’s not just a nerd who gets good grades in his science classes. He’s a genius nerd with ambitions to become a scientist. This side of Peter---and Spider-Man---isn’t missing from Tobey Maguire’s Spidey---and Peter Parker---it’s just not a side of his character we see in action, except where it’s needed to move the plot along in Spider-Man 2 and 3. But The Amazing Spider-Man devotes a lot of time to establishing that Andrew Garfield’s Peter has more than just an aptitude, he has an already mature ability to do the science. As much time as it spends on re-telling the origin story. In fact, it’s integral to the origin story. This is useful because Garfield’s Spidey has to make his own webbing. It’s important because Spider-Man---the comic book hero---spends many a book thwarting the evil plots of mad scientists and that requires him to do SCIENCE!
Or “science”, at any rate.
Which is what goes on in The Amazing Spider-Man.
In Spider-Man 2, Spidey mostly deals with Doc Ock as a bank robber and hostage-taker. Peter’s being a good student of science is the basis for his getting to be friends with Otto Octavius and that happens in order to make the audience sympathetic to Octavius. The “science” doesn’t really matter. The science experiment gone haywire at the end is just a bomb Peter and Octavius defuse in the nick of time.
The science, goofy as it is, matters in The Amazing Spider-Man. Which means it matters that Garfield’s Peter Parker is a scientist to a degree it doesn’t matter with Maguire’s.
That doesn’t make Garfield’s portrayal better than Maguire’s. Just different in a good way.