Criticizing the movie by saying its the same as the 2002 film is pretty cheap. While the movie does have flaws and isn't a solid film on its own, it is very different from the first Sam Raimi film. Naturally there will be similar plot points, such as Peter getting bit by a spider, a speech about responsibility, uncle ben dying, Peter becoming Spider-Man, etc. There are more differences than similarities between the two movies.
If you just glance at the two films, then you might say they are the same. If someone dislikes the film just for that reason, they have every right. But IMO its their loss.
I see what you're saying and thats what I thought after the first time I saw the movie too but then I noticed how many plot points it hits that the Raimi film does outside the origin.
*We're introduced to Peter and he gets humiliated, the girl coming to the rescue (SM1: Peter can't catch the bus and MJ tells the driver to stop, AMS: Gwen makes Flash stop beating him up.)
*Peter goes to a laboratory and meets the antagonist who recognizes his intelligence. (SM1: Norman runs to give Harry his backpack and tells is introduced to Peter, who he is impressed understood his scientific publications. AMS: Peter sneaks into OsCorp and is the only student in the group that can answer Dr.Connors question.)
*SM1: Peter gets bitten by a spider with a group of students following a tour guide, and breaking the rules talking to a girl. AMS: Peter gets bitter with a group of interns breaking the rules, leaving the group.
*Peter gets bitten by the spider after having a conversation in the lab with the love interest in both films.
*After getting bitten Peter starts a fight (SM1: accidentally hitting flash with the tray. AMS: Accidentally ripping the womans shirt off)
*When he gets home he freaks out Aunt May and Uncle Ben before going right to sleep. (SM1: Tells them he's not feeling well and runs straight to bed, while Ben and May discuss if this is normal. AMS: Peter acts like hes destroyed and takes everything in the fridge up to his room, May and Ben discuss if it's drugs.)
*Peter wakes up and finds he's different. (SM1: corrected vision, huge muscle development, hand stick to the bus, ect. AMS: Breaks the bathroom and alarm clock.)
*Peter realizes the Spider caused these changes. (SM1: looks at the bite on his hand. AMS: finds the spider)
*Peter gets a speech about responsibility, BOTH because of what happened between him and Flash and him not doing a favor he asked. (SM1: Painting the kitchen, AMS: Picking up Aunt May.)
*Uncle Ben gets shot in the street and Peter is there too see him die. Note in the comics he died in his house and Peter came home to the investigation, this is not necessary.
*We see proto Spider-Man costumes and right when he appears we see, a public figure declare war on Spider-Man. (SM!: Johan Jameson. AMS: Captain Stacy.)
*The villain intends on making a serum to better human anatomy. (SM1: Norman Osborn the Super Soldier Serum, AMS: Dr.Connor a serum to regrow limbs and cure terminal aliments.)
*The villain isn't ready but his superior gives him and ultimatum to present human tests or lose his career. (SM1: Osborn was going to lose the defense contract bankrupting OsCorp, AMS: Raffa was going to close his research department and continue without him.)
*The villain ultimately decides to test the formula on himself.
*The villain attacks the person that gave them the ultimatum. (SM1: Osborn kills the General and the Quest technicians. AMS: Connors goes after Dr.Raffa.)
*The villain comes into conflict with Spider-Man seeking revenge for being forced out. (SM1: Osborn attacks the board of directors at the parade. AMS: Connors attacks people on a bridge looking for Raffa.)
*The villain gets in a fight with Spider-Man wounds him and finds out his identity. (SM1: Osborn cuts him with a razor bat and deduces it at dinner. AMS: Connors cuts Peters chest and finds a camera with his name on it.)
*The villain rushes back to his respected liar and his two personalities argue over what to do about Peter Parker being Spider-Man.
*A police officer tries to arrest Spider-Man until he sees he is needed to save someone. (SM1: Woman in the burning building. AMS: Gwen.)
*The scene immediately following the defeat of the villain is a funeral. (SM1: Osborns. AMS: Captain Stacy)
*Peter has to make the hard decision to not see the love interest anymore taking the high road of responsibility. (SM1: Peter has to tell MJ he can't be with her and lies saying he doesn't love her. AMS: Peter tries to make Gwen not see him anymore and ends it.) Note both follow the funeral.
*Finally we have the call back to Uncle Ben. (SM1: Peter looking at his tombstone. AMS: Peter listening to his last voicemail he left him.)
Look I liked Amazing Spider-Man and I don't think it was a bad movie, but the complaint that it was very similar to Spider-Man 2002 is a legitimate complaint that extends beyond the origin story aspects.
EDIT: just read the end of that. Yeah I agree it is there loss, but my point was there were similarities. I feel like when they made this movie they almost had a check list of everything people complained about from the Raimi films and tried to be different.