Both are perfectly fine for payments, I would say. However, it still depends on what you are currently holding. I mean, if a person uses bitcoin as store of value, then he might choose to make payments in the same asset. Otherwise, he will need to exchange it for another cryptocurrency like Ethereum to make a transaction.
Yup unless you got a wallet which holds mulitiple coins. It decreases the time and hassle you spend from the process of converting through the use of an exchange. But to be honest, I still stick to btc though I am using such kind of wallet. I don't actually mind if eth is the obvious better option here because I already got used to btc. I'm satisfied with its speed and I can't feel the fees also. For me a 1% fee is not so big. Well, I guess maybe that's because I only withdraw small amount of money and my opinion change once I withdraw bigger 
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