Native English UK Reader here and whilst the words have essentially the same meaning, I would definitely have a different take away from these two:

- John is a nice guy, but he beats his dog.

- John beats his dog, but he's a nice guy.

For me, the difference is that the second one carries more of an implication that the speaker doesn't consider dog beating all that problematic since even though John does it, he's still a nice guy. Also, to me, the first one is more judgemental towards John than the second.

This is even summed up in a bit of wisdom: in a sentence containing the word "but", you may safely ignore everything which comes before that word.

Non-native speaker here. I read it as an emphasis on the second part. First sentence makes a point that John deserves judgement, the second one that he deserves leniency, on the net balance of his qualities.

Indeed there’s no difference. There’s a possibility of different emphasis, but it would depend on a wider context.

I had the same response as you. I’ve come to accept that not everyone’s brain is wired the same.

Yea... they all mean the same thing. I think they're trying to split some imaginary hairs.