You really think they sound very different? What you have here is a well-spoken American and a well-spoken Brit. Their accents are obviously different, but they are not so far removed from each other. 

@Paul I understand what they say, they have a clear accent. But, I've heard different pronunciation in some words and expressions.
I know you don't want to criticise. Nevertheless, the difference can be noticed more when you are a non-native speaker, although the accents are not far.

@Elia yes, in the article you were talking about the meaning of some words, and in the video they discussed it and is quite interesting, but when I've watched it, I've lent more attention on the accents.
Why? I don't know. But it also can be a little difference.

I think that this is what Anna was trying to say. Although their accents are standard (because they speak really well), you can notice differences. The article focused more on words that mean different things in BrE vs AmE. I am familiar with American accent and I know this is nothing compared to the real world.

I hope that doesn't come across like I'm criticising by the way. If they sound very different to you then who am I to say differently. But to me, despite one obviously being American and one being British they don't sound that different.

@anna I totally agree with you.