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 
. I think that's one factor why many people are still using btc even if eth has lower tx fee. If they have btc in hand and suddenly they need to pay or buy something, instead of going to convert it to eth first, they will just directly use btc as converting will consume time, so it is more of convenience that we are talking here. But if you already have eth available, why not?