It was NEITHER. The good news is that the Jewish family from Frankfort who renamed themselves the Rothschild family, never had a red Star of David for their Family Coat of Arms. The bad news is that their authentic Coat of Arms wasn’t a normal-shaped red shield either. The name Rothschild (Red Shield in German) originates from the description of the family house located in Frankfurt’s Jewish Ghetto and known to neighbors and residents as the house with the red shield. The whole story goes something like this-
The ancestry of the Rothschilds can be traced back to 1577 to Izaak Elchanan Rothschild (Isaac (Isaak) Elchanan Bacharach, zum Hahn), whose name derived from the house he occupied in the Judengasse-zum roten Schild (“at the sign of the red shield”). His grandchildren and descendants took this name as the family name and kept it when they relocated in 1664.
– Mayer Amschel Rothschild, WikipediaThe Coat of Arms of the Jewish family from Frankfort who at some point had lived in a Frankfurt house with a big red shield hanging near the entrance, was rather complex and may not have even been their original Jewish Coat of Arms before they changed their last name to Rothschild.
I researched this question on my own quite thoroughly quite a few years back and found that there wasn’t any evidence that the Rothschild clan ever used the Jewish six-pointed Star of David in their own family’s emblem. In fact, the internet shows the official Rothschild family crest to be a 4 part shield held up on each side by a Lion and a Unicorn. Above the sdhield hangs a three part bundle of armored headpieces. Just above the armored headpiece on the left is a six-pointed Star decoration that LOOKS NOTHING LIKE THE JEWISH STAR OF DAVID. So. if you are looking for conspiracy theories that are even partially true, it’s best to give up on the Rothschild family conspiracy as soon as possible. There’s just nothing there.