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I guess this is caused by the fact that Dutch has no good one-word translation for allow, so it will be described. Translating the description back gives this result.
why did you translate them to Dutch then back to English?
I gave it as an example. My question is about how to correctly translate the Dutch version to English. The dutch lack of one word for 'allow' makes the choice for 'allow' less likely. But does that make it good English? Some Dutch ways of expressing should NOT be translated literally. Is this one of them?
While they are both correct, it depends on what you're writing. If you are writing anything where you don't need to beef up the word count/length, then you can use either. However, in most writing, especially business, science, and websites, being concise is better. In that case, use "allow" if you can. A lot of English speakers or learners will see the longer sentence, be concerned that they don't know what all the words mean, and then go away. "Allow" fixes that entirely.
To add to what Laura says, if your context is technical documentation of any sort, go with the standard English way of describing the particular action. In this case, "the system allows the user to log in" is more direct. The other sentence, while grammatically correct, sounds unnecessarily roundabout. It sounds like directly translated text. Depending upon the context (the type of document, the audience, the nature of the section within the document, the particular passage), even "the system allows the user to log in" might be better rephrased in some other way.
You wrote: "The other sentence, while grammatically correct, sounds unnecessarily roundabout.". This is precisely the feeling I got with this sentence, but then I am not a native speaker of English, so I could have been wrong about this. I am glad my hunch has been confirmed. About rephreasing some other way: I can think of one more: "the system enables the user to log in". Or the original line that triggered this question: "This contest gives the students the possibility to show their talents". My preference would be: "This contest allows the students to show their talents". Or would "enables" be even better here?
Again, it really depends upon the context. It is difficult to work with one sentence in isolation. In reality, you often phrase so that the sentence in question fits in well with the surrounding sentences. That is, you consider local clarity (in the sentence) as well as cohesion (of the passage), and balance the requirements of one against the other. For this particular sentence, depending upon context, you might go with one of these -- This contest gives students the opportunity to show their talents. This contest offers students the opportunity to show their talents. This contest gives/offers students the opportunity to display their talents. as well as any number of other variations. In the original, the word "possibility" does not sit quite right, but the structure of the sentence itself is not problematic. Your rewrite is shorter, but somehow "allows students to show" does not work as well, I don't think, as "gives students the opportunity to show," and I'm not sure why. That's the sense I have, at any rate. Note too I've removed the article ("the") in front of students. Depending upon context -- which students these are, who the audience is -- this might work better.
Thanks for the clear explanation.