One or the Other: Rabbi Yishmael Omer

I recently received an e-mail asking about the proper text in the "Rabbi Yishmael Omer" passage we recite at the end of the korbanos section of the morning prayers. The standard text in most prayerbooks is (translation from the new Koren Sacks Siddur):

כל דבר שהיה בכלל ויצא לטען טען אחד שהוא כענינו יצא להקל ולא להחמיר
כל דבר שהיה בכלל ויצא לטען טען אחר שהוא כענינו יצא להקל ולהחמיר

When a particular case, though included in the general statement, is expressly mentioned with a provision similar to the general law, such a case is singled out to lessen the severity of the law, not to increase it.
When a particular case, though included in the general statement, is expressly mentioned with a provision differing from the general law, it is singled out to lessen in some respects, and in others to increase, the severity of the law.

Note that there are two very similar words in the Hebrew -- echad (אחד - one) and acher (אחר - other).

Click here to read moreNote that there are two very similar words in the Hebrew -- echad (אחד - one) and acher (אחר - other). That is how the Artscroll siddur has it and, to my knowledge, most others. I checked Dr. Seligmann Baer's classic Siddur Avodas Yisrael and it has it that way also. However, the Birnbaum and De Sola Pool siddurim have both of them as acher. Which is correct?

My theory is as follows:

The source of the "Rabbi Yishmael Omer" passage is the beginning of the Sifra, an ancient halakhic midrash. The texts we have of the Sifra have both words as acher. However, for whatever reason, all of the prayerbooks have the words as echad and acher. Most of the prayerbooks -- including Artscroll and Koren -- want to continue the prayerbook traditions and therefore maintain the difference. Birnbaum and De Sola Pool thought they would correct it based on the source (note that the De Sola Pool prayerbooks' Hebrew was established by R. Chaim Dov Chavel, of Ramban fame).

A correspondent was kind enough to look up the commentary in the Siddur Eizor Eliyahu, whose author investigated old prayerbooks in order to establish the exact prayerbook that the Vilna Gaon used. Interestingly, the first edition of Siddur Eizor Eliyahu had both as acher, like the Sifra, Birnbaum and De Sola Pool. But my correspondent did not stop there. He check the second and third editions, which have it differently. Beginning with the second edition, the Siddur Eizor Eliyahu changed it so that the first is echad and the second is acher. The commentary says that this is the way all of the old prayerbooks have it, and R. Wolf Heidenheim and Dr. Seligmann Baer as well.