The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that the section of Hodu should be recited in the morning immediately following the Korbanot section, which discusses the sacrifices offered each day in the Bet Ha'mikdash. King David established the reading of Hodu during the offering of the daily Tamid sacrifice, and so, in commemoration, we should recite Hodu immediately after we speak of this sacrifice. Furthermore, the Ben Ish Hai writes, the declaration of "Hashem Melech, Hashem Malach, Hashem Yimloch Le'olam Va'ed" should be made soon after the recitation of Hodu. Therefore, if somebody recited the sections of Korbanot and Hodu at home, and then comes to the synagogue, he should repeat Hodu so he can juxtapose this recitation to the pronouncement of "Hashem Melech…" Our custom is to recite Hodu before Baruch She'amar, but the custom among many Ashkenazim is to recite Baruch She'amar first, before Hodu. This sequence is indeed found in a number of ancient Ashkenazic texts of the Siddur. The Maharam Shick (Hungary, 1807-1879) went so far as to say that one who recites Hodu before Baruch She'amar does not fulfill the obligation of Pesukeh De'zimra. He explained that the verses of Hodu express praise for Hashem, which is the function of Pesukeh De'zimra, and so they must be included within the framework of Pesukeh De'zimra, which begins with Baruch She'amar. Later Rabbis disputed this strict position, noting that the Arizal taught that Hodu should be recited before Baruch She'amar. Moreover, even the Ashkenazim recite the chapter of "Aromimcha Hashem Ki Dilitani" before Baruch She'amar, even though that chapter, like Hodu, expresses praise to Hashem. And, several Rishonim wrote explicitly that one should proceed directly from Baruch She'amar to the series of "Haleluya" chapters of Tehillim, such that Hodu must be recited beforehand. Of course, every community should follow the custom that they've received from their forebears. The Arizal taught that every community has its own "gate" through which its prayers ascend to the heavens, and so each community should strictly adhere to its customs. Significantly, however, Hacham Ovadia Yosef cites the Hida (Rav Haim Yosef David Azulai, 1724-1806) as stating that prayers that follow the Sephardic custom ascend through all the "gates," and thus an Ashkenazi who wishes to adopt the Sephardic prayer customs may do so. This is evidenced by none other than the Arizal himself, who was an Ashkenazi but decided to adopt the customs of prayer followed by the Sepharadim. Similarly, Rav Natan Adler (Germany, 1741-1800) brought a Rabbi from Turkey to teach him the Sephardic tradition of prayer because he wanted to adopt those customs. Therefore, Hacham Ovadia writes, an Ashkenazi may switch to the Sephardic prayer customs, but a Sephardi may not adopt the Ashkenazic prayer customs. Accordingly, Hacham Ovadia ruled that if a Sephardi prays in an Ashkenazic Minyan, he should not serve as Hazan, as this would require him to recite Baruch She'amar before Hodu. Hacham Ben Sion Abba Shaul (Jerusalem, 1924-1998) maintained that a Sephardi may lead the services according to Ashkenazic custom, but Hacham Ovadia disagreed, and stated that a Sephardi must adhere to the Sephardic custom of reciting Baruch She'amar only after Hodu. If a Sepharadi mistakenly recited Baruch She'amar without first reciting Hodu, and he realized his mistake after completing Baruch She'amar, then he should recite Hodu at that point. This was the ruling of Hacham Ben Sion, and Hacham Ovadia would presumably agree that after the fact, if a person already recited Baruch She'amar, then he can and should still recite Hodu. Summary: Sephardic practice is to recite Hodu before Baruch She'amar, whereas many Ashkenazim have the custom to recite Hodu only after Baruch She'amar. A Sepharadi praying in an Ashkenazic Minyan must adhere to Sephardic practice, and so he should not serve as Hazan, as this would compel him to reverse the order in accordance with Ashkenazic practice. However, if a Sepharadi mistakenly recited Baruch She'amar first, he recites Hodu afterward.