To add to what FlickChick wrote, the Caretaker character was
completely different. Reeves did this with a simple shot of a decades-old picture and a couple lines of dialog (after his botched kill attempt). In the original, you don't care about him at all. His death does not mean as much. In Let Me In, he is more sympathetic and his death is poignant. Summing up, he goes from a pedophile to a lifelong companion. That's a
big difference.
Reeves also added several Hitchcock type elements to the movie. The
Rear Window stuff is pretty obvious...but also the scene with the Caretaker in the backseat of the car and the scene when the cop breaks into Abby's apartment are worthy of the Master of Suspense.
Then there is the fact that Reeves changed the
gender of the vampire character. Hard to change a character more than that.
Reeves dropped several characters completely. (And you don't miss them...so that tells you how important they were in the first place)
The Owen character is more sympathetic too due to his desire to be a serial killer being downplayed.
Due to many of these changes, the ending felt different for me. Less happy, but more to think about. Was Owen fated to follow the same path as his predecessor? Or is he going to be different? The reason being that Oskar and Hakan are
very dissimilar characters while the Caretaker and Owen could possibly be the same boys separated by 4 decades.
The "shot for shot" case...well...that is disproved with...the
first shot of the movie.

t:
Two great movies that each bring something different to the table.