if it's a security issue I think both are safe. the only difference is that BUSD is on the Binance network, while USDT is not.
I think it's just personal preference to choose USDT or BUSD because they are functionally the same, and are not affected by a decrease or increase in market prices.
I think there is a massive difference between the two and that is the fees. Getting your USDT from one exchange to another right now costs you a fortune. The fees are ridiculous. Some exchanges charge up to 20 USD for a single USDT withdrawal. The issue is that not all exchanges have BUSD listed. Anyway, if you stay on the ETH network USDT is just fine even though the fees are still a pain in the ass, but if you have the choice I would go with BUSD as it gives you more flexibility financially.