The answer to your question is both and neither. Allow me to explain:
Chabad, as well as all other chassidic groups, finds its roots in Eastern Europe, which was the home to much of Ashkenazic Jewry. As such, initially, most of Chabad’s adherents were of Ashkenazic origin.
Historically, however, Sephardic Jews were always more mystically inclined than their Ashkenazic brethren, as evidenced by the fact that the majority of the famed Jewish mystics were Sephardic. Thus Sephardic traditions and customs have always placed greater emphasis on the mystical, and are more in line with Kabbalistic tradition.
Chassidism in general, and specifically Chabad Chassidism, places a great emphasis on Kabbalistic teachings. For this reason, the Baal Shem Tov, founder of the Chassidic movement, incorporated many Sephardic traditions into the primarily Ashkenazic practices of his Eastern European constituency. Many of these differences involved the order and wording of the prayers.
Since chassidic tradition incorporates many elements of Sephardic tradition, the prayer text used by chassidim actually came to be known as nusach sephard (“Sephardic version”), while the prayer text of the “real” Sephardim is commonly referred to as nusach sepharadi (prayer version of the Sephardic Jews), or nusach edot hamizrach (version of the eastern communities).
So the answer is that, for the most part, Chabad tradition was always Ashkenazic with a Sephardic twist.
I would point out that although Chabad did originate in Ashkenazic lands, the philosophy of Chabad is not any more Ashkenazic than it is Sephardic. The core principles of Chabad—the focus on chochmah, binah and da’at (wisdom, understanding and knowledge), in one’s service of G‑d—are equally important to all Jews. Today there are many Sephardic Jews affiliated with Chabad, many of whom have maintained their Sephardic backgrounds and complemented them with Chabad teachings and traditions.
Indeed, the Rebbe was asked several times by Sephardic Jews who had adopted chassidic practices whether they should alter their Sephardic Hebrew pronunciation in favor of the Ashkenazic pronunciation prevalent amongst Ashkenazic chassidim. The Rebbe responded that there is no reason for them to do so; to the contrary, he advised them to maintain the traditions of their ancestors.
Rabbi Menachem Posner