What is the right place to acknowledge another (simultaneous) paper with the same result?

Τhe sections of Introduction and Related Work of a paper serve the purpose to inform the reader exactly about related results/attempts/techniques etc in order to put their result in the correct perspective. As such, the "other" result should be mentioned and cited there, preferably with a direct comparison of the possibly different techniques involved. Anything else, could be potentially misleading and/or suspicious and should be avoided.

I have been in this situation as an co-author. Before the acknowledgements, at the very end of the conclusions we wrote:

Note added.—Recently, we have become aware of Ref. 22, where a similar approach to ... has been undertaken for ... —and analogous conclusions have been reached regarding ...

They also wrote something similar at the end of their paper. The story was that we submitted to the arxiv within the same week. The papers were almost identical (I think they redid the calculations with our parameters to check if they get the same). In the end, their paper got accepted quite quickly, while in our case, the editor dragged us for one year and half.

I have seen papers that were in a slightly different situation than yours: on the cusp of going to print when a similar paper made its first appearance (on arXiv or in a journal if it didn't get put on arXiv first). These papers often include a small paragraph at the end of the paper, immediately before the acknowledgments section, citing the paper, summarizing the results, and include a statement such as "this paper was published as we were going to print".