Actually, it's rare to use them. But sometimes, BUSD is used moreover when using Binance or their partner, some pairs are available only in this stable coin.
Both BUSD and DAI have different sides of positive and negative. We can at least consider what is best for us in trading pairs. However, if this is about keeping for long-term holding, I will prefer BUSD because this is from Binance. However, so far, I am using USDT to do most trading pairs because this is more general and used in some exchanges
But, USDT is now also available in some networks such as BSC and also Tron network as the most affordable networks available to send USDT at lower fees. Using the networks will save enough the fees compared with using Ethereum network or Omni