For trading, using USDT is a lot better because it is commonly used on many crypto exchanges. There are also a lot of pairs using that stablecoin than the others. While BUSD is only exclusive to binance and have only few pairs to trade in BUSD/alt.

In terms of safety, the popular stablecoins that we have now is backed by a private entity and each of them have their own flaws so what I do is I diversify my holdings into USDT, USDC, and BUSD.