I wasn’t aware that the menora was different is the 2 batei mikdash, interesting. I know we have an image of the menora from Titus’ Arch, assuming that it is a depiction of The Menora, and not just any menora, And chabad holds that the menora had straight branches, V shaped. But I thought the matter is still up to debate.
The point is not to replicate the menora of either beis hamikdash (an exact replicate is assur, actually) but to light in any vessel that fits the halachic criteria. Either menora you describe does not: the menora in the beis hamikdash had 6 side branches turning toward the middle main branch, for a total of 7. Since we light 8+1 shamash, the chanuka “menora” is obviously different.