Chabad-Rambam Menorah:

The commonly depicted shape of the Menorah contains curved half circle branches, and is used for coinage, marketing, designs and sculpture art. The Rebbe[1], after a thourough Halachic and historic analyzation, concluded that this shape is in truth not the shape of the Temple Menorah, but of a cloned Menorah which was captured by the Romans, and placed on display in Rome to depict the fall of the Jews. The true shape of the Temple Menorah, from both a Halachic[2] and Historic perspective, contained diagonale branches. This is the shape of the Menorah which was depicted by the Rambam in his magnum opus Mishneh Torah, and was testified by his son, Rav Avraham, to be an exact depiction of the Temple Menorah. Due to the Rebbe’s discovery and revelation, artists commonly name this Menorah as the Chabad Menorah, although in truth this is the Menorah of all Jewry, as depicted by the Rambam. The Rebbe stated that one one is to endeavor to use for Chanukah an eight branch Menorah which follows the true Temple shape, and not the half circle branches which depict a cloned Menorah which was used by the Roman’s as propaganda for crushing the Jewish pride and spirit.[3] [This however does not mean that everyone should use a Temple shaped Menorah, but that if they are buying a Menorah with branches, then the branches should be diagonal. However, Menorah’s that do not contain branches may also be used, and so was used by the Rebbe himself.[4]]

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[1] Likkutei Sichos 21:168 and 26:201 [printed in Shulchan Menachem 7:192]

[2] Depiction of Menorah of Rambam brought in Pirush Hamishnayos and Hilchos Beis Hebchira 3:10; Rav Avraham the son of Rambam on Parshas Teruma 25:32 “The six branches come out of the main branch in a diagnole, as my father depicted, and not in a half circle, as is depicted by others”; Rashi Teruma 25:32 “The branches are diagnole”; See Bechor Shur Rosh Hashanah 24 and Mishnas Chachamim Avoda Kochavim p. 64, brought in Pischeiy Teshuvgah 141:14 who implies the Temple Menorah had diagnole branches

Other opinions: Some sources record that the Menorah contains half circle branches. [Maaseh Choshev 7; Chochmas Hamishkan; Zayis Ranan Behalosecha; Even Ezra Tetzaveh 27:21; Teruma 25:37]

[3] Likkutei Sichos 21:168 footnote 41 [printed in Shulchan Menachem 3:275]

[4] Hiskashrus 541:12 footnote 9