With all due respect to Rav Ovadia, I am extremely suspicious of him. In general, however much he champions Sephardi halakhah, his general hashqafa seems Haredi. Anyone who worked with Rav Shakh (as Rav Ovadia did), I'm very suspicious of him.
I bring one random example, even though one could write a volume on this: Rabbi Ovadia: 'Women should stick to cooking, sewing':
Yosef blasted the opposing view, saying it was based on the opinion of "a few stupid women. A woman's knowledge is only in sewing," he ridiculed. "Women should find other jobs and make hamin (cholent) but not deal with matters of Torah."Rav Ovadia's low opinion of women, and his cultish subversion of family tradition in favor of an elitist textual opinion, both bespeak a very Haredi attitude. (The Haredim are well-known for engaging in historical revisionism, erasing and subverting family mimetic tradition in favor of untraditional and unhistorical practices derived from elite ivory-tower textualism. Many Haredi magazines and pamphlets after the Holocaust urged children to disregard their parents' traditions and teachings and instead follow the gedolim; Rav Ovadia is simply following a well-paved path.)
In addition, he admonished women for following in the steps of their mothers in the order of the recitation of the blessing instead of adhering to his opinion.
"It has to be announced that women should not listen to the voice of their mothers or grandmothers not to continue with this mistake," he warned.
(The above quotation also indicates Rav Ovadia's attempt to unify all the disparate Sephardi and Mizrahi minhagim, trying to unify them all under the aegis of the opinions of Rabbi Yosef Karo, even when individual Sephardi/Mizrahi communities had differing customs. See the reference to "Skeptic" and Professor Marc Shapiro below.)
In the words of Daniel Elazar (Can Sephardic Judaism be Reconstructed?),
The death of Rabbi Uziel marked the final takeover of power from the Sephardim by the Ashkenazi rabbinical establishment. ...
The Sephardic Chief Rabbinate had been the preserve of the Spaniolim [i.e. Ladino/Judeo-Spanish Turkish Jews], who be the early 1950s were thoroughly outnumbered by Asian and African [i.e. Mizrahi] olim. In the struggle over who would be appointed to succeed Rabbi Uziel, the Ashkenazi rabbinical establishment threw its backing behind Rabbi Yitzhak Nissim of Iraqi origin, who was opposed by the Spaniol establishment. Rabbi Nissim won, with Ashkenazi votes, which put the Sephardic Chief Rabbinate in a clearly subordinate position, de facto, to the Ashkenazim, a position in which it remains to this day, although one of the selling points of Shas, the Sephardic Torah Guardians, and its spiritual mentor, former Rishon Le-Zion, Rabbi Ovadia Yosef, who is recognized as one of the great posekim (halakhic decision-makers) of our day by Ashkenazim and Sephardim alike, was that the Sephardim had to take back their rightful position.
Unfortunately, Rabbi Yosef and his colleagues had themselves become so Ashkenazified through their education in Ashkenazi or Ashkenazified yeshivot that, while they in fact regained some power, they did not offer very much of an alternative. Rabbi Yosef, also of Iraqi background (since the election of Rabbi Nissim, all the Sephardic Chief Rabbis have been of Iraqi background), feeling the pressure of the Ashkenazi yeshiva heads, consistently refused to provide support to the Sephardic community's efforts to establish more open yeshivot in the 1960s and 1970s.
*** Update: "Skeptic" in the comments below has rightly pointed out that I should make reference to Professor Marc Shapiro's review of several biographies of Rav Ovadia, here. As far as I remember, this article only summarizes (1) Rav Ovadia's rise to the political and scholarly position he now occupies (his childhood, his education, his relationship with Rav Shakh, etc.); (2) His crusade for Sephardism (teaching Torah in the Bukharian market, founding Shas, etc.); (3) His general relationship to various Sephardi poseqim and schools of halakhic thought (Shulhan Arukh, Ben Ish Hai, Rabbi Mordechai Eliyahu, etc.), and his relationship to various disparate Sephardi minhagim and communities (Iraqi, Moroccan, etc.); (4) His controversial statements on matters of politics and culture (the Holocaust, etc.). As far as I recall, this article contains nothing that would support my thesis that Rav Ovadia is "Ashkenazified" (except for his relationship to Rav Shakh, which by itself is insufficient to make a case), but be that as it may, for this article, one way or another, contains much valuable information.
*** Update: also, as "Skeptic" points out, Rav Ovadia is far more complex character than I here give him credit for. Actually, this was my intent in saying I am "suspicious" of him (I'd use far stronger terms regarding bona-fide Ashkenazi Haredim). I'm suspicious of Rav Ovadia, and ambivalent about him, whereas I am enthusiastic for the German Neo-Orthodox and the traditional Moroccans and Judeo-Spanish and the Modern Orthodox, and I am downright disgusted with and repulsed by the Ashkenazi Haredim.