There is a major disagreement between the Poskim regarding how many Berachot are recited before putting on Tefilin. Rabbenu Tam )R. Ya’akob b. Meir, 1100-1171, France) and the Rosh (Rabbenu Asher Ben Yehiel, 1250-1327, Germany-Spain) rule that two Berachot are recited, one on the Shel Yad (Tefilin of the arm) and one for the Shel Rosh (Tefilin of the head). They hold that they are two distinct Misvot, requiring a separate Beracha on each.
On the other hand, the Rif (Rabbi Yishak of Fez, Morocco, 1013-1103), as well as Rashi and Rambam disagree and hold that only one Beracha of "L’haniah Tefilin" is recited before the Shel Yad, and that covers both.
Both sides bring a proof to their position from the same Gemara in Menahot. The Gemara states that if a person spoke in between putting on the Shel Yad and the Shel Rosh, he must make a Beracha on the Shel Rosh. From here, Rashi derives that one makes a special second Beracha on the Shel Rosh only if he spoke, but ordinarily there is only one Beracha. Rabbenu Tam interprets the Gemara in line with his position. He says that of course one always makes a Beracha on the Shel Rosh. The Gemara is saying that if he talks, he now has to make two Berachot on the Shel Rosh, since he interrupted the first Beracha made on the Shel Yad.
There is disagreement as to what Rabbenu HaAri’s opinion was. The Ben Ish Hai writes that the Arizal explained the reasoning for each opinion, but did not rule in favor of one practice. The Kaf HaHaim writes in SIman 25 that he has proof from Sha’ar HaKavanot that the Arizal held like Rashi and the Rif.
This disagreement evolves into divergent practice between Ashkenazim and Sepharadim. The Sepharadim follow the opinion of the Rif and Rambam that only one Beracha is recited. The author of the She’elot U’Teshubot Min Hashamayim (Responsa from Heaven, Rabbi Ya’akob of Mirvish, d. 1243) would ask a Halachic question of the Heavens before going to sleep and would receive answers in his dream. When he asked whom to follow in this question, he saw the Pasuk "And I will establish my covenant with YISHAK." He understood from this that the Halacha is in accordance with the Rif-Rabbi YISHAK Alfasi. That is the accepted practice.
The Bet Yosef cites the Rabbenu Ya’akob b. Habib who says that those who recite two Berachot should say, "Baruch Shem K’vod Malchuto L’Olam Va’ed" after the second Beracha. This is meant to alleviate the possibility that the second Beracha was said in vein. The Bet Yosef, after paying respect to this opinion, says that it is hard to understand. If the Ashkenazim have a genuine uncertainty whether to say the second Beracha, they must refrain from making the doubtful Beracha and not risk saying Hashem’s name in vein. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) answers that saying "Baruch Shem…" is just a Humra, and not really because of a doubt. There ae enough authorities to rely on who rule in favor of saying the second Beracha. Interestingly, saying "Baruch Shem…" became the accepted practice of the Ashkenazim.
The Be’ur Halacha (Rav Yisrael Meir Kagan of Radin, 1839-1933) cites Rabbi Akiva Eger (1761-1837) who suggests in his glosses to Shulhan Aruch a way for Ashkenazim to recite the second Beracha without entering a Halachic uncertainty. He says that they should say the first Beracha on the Shel Yad with explicit intent that it should NOT cover the Shel Rosh. The Peri Megadim objects to this solution, but does not explain why. The Be’ur Halacha explains that the Peri Megadim objected because it is changing a long standing Minhag (custom). For generations, Ashkenazim recited two Berachot on Tefilin and said "Baruch Shem…" If there was a better way to do it, the giants of the previous generations would have already done so.
The Poskim discuss whether a Sepharadi may answer Amen to an Ashkenazi’s second Beracha. Hacham Bension rules that there is no problem since it is a legitimate Beracha for the Ashkenazi reciting it. This ruling applies to other cases where an Ashkenazi recites a Beracha that Sepharadim do not, such as Hallel on Rosh Hodesh and a Beracha by women on the Lulav. It is important to note that this was also the opinion of Hacham Baruch, even though Hacham Ovadia disagreed. Hacham Ovadia held that any Beracha that one cannot make for himself is considered a Beracha L’vatala (in vein), and he should not answer Amen to someone else who makes that Beracha. According to him, one should not answer Amen to an Ashkenazi’s second Beracha, nor to Hallel on Rosh Hodesh and a woman’s Beracha on the Lulav.
L’Ma’aseh, one can adopt a compromise suggested by Hacham Bension. He can avoid the issue altogether by synchronizing the end of the other person’s Beracha with saying the Pasuk "Baruch Hashem L’Olam Amen v’AMEN," which ends with Amen. However, if one did not do so, he MAY answer Amen, in accordance with Hacham Baruch
SUMMARY
A Sepharadi may answer Amen to the second Beracha recited by an Ashkenazi on his Tefilin, as well as to all other Berachot which Ashkenazim recite, but Sepharadim do not.
