A few questions I have to answer before giving a my opinion.
Does a remake always have to have the ambition to be better than the original? No
Is "broader audience" enough of a reason to make a remake? Yes
Does language affect the impact of the movie? Maybe
Have I already decided that the original is better than the "copy"? Maybe
One could argue that if you are going to do something that's already done, you better do it better. While this might be true in many cases I don't necessarily think this needs to be true when making a remake. Of course it's desirable, but there are other reasons that can motivate a remake. A broader audience can be one. This is often linked to language. The USA is the biggest producer of movies in the world. Even though there are plenty of Bollywood movies out there, there is really no comparison when success is measured in box office numbers.
The formula is really simple. A good movie is made in a foreign language (or British English, such as "Death at a funeral") and is proven to be successful. Rewrite the script and add some "Hollywood flair" (and Hollywood actors) and launch it as a Hollywood production. Then wait and hope the movie will be a success and make tons of money.
How big is the language impact? I'm not surprised that I enjoyed the Swedish version more than the American version. Swedish is my first language and I assume I understand the subtle nuances better even though my English is fluent. But then there are many other movies where I don't understand the original language at all, but still found them better than the English remake. This leads me to the final question I posed earlier. Will I always think the original is better than the "copy"?
I've looked through an extensive list over remakes and I can't find a single movie where I preferred the remake. So, do I intrinsically prefere the originals or am I just more intrigued by other perspectives than the Hollywood one? Don't get me wrong, some of my favorite movies are big Hollywood productions, but maybe we should put more effort in promoting the already good originals rather than remake and relaunch. But on the other hand, I believe many people prefere the remakes because they are usually more accessible. And if there was no audience, there would not be a market for remakes.
Let's go back to discussing "Let me in". This movie is essentially a coming of age, vampire movie. But it has very little in common with Twilight and True Blood. You don't need to be a teenager or vampire fan to enjoy this movie. It's mostly about relationships, emotional struggle and a very lonely vampire. And the remake aspect of it? I was pleasantly surprised. They stayed pretty true to the esthetics of the original movie. They invited Swedish producers. The plot is still great and the casting was mindful. I will still recommend the original before the remake, but for those who choose to see the remake, they will have a great movie experience.