If I had to choose between the two, it would be the doge. The project itself was the well-known meme coin in its own right. But in the last months because of Musk doge is treated as a pump-dump coin.
As for the Shib issue, I do not understand what Shiba is and why it is supported by Binance and other big exchanges too. The society that wants to support dogs should support outsiders, not them.