Hi  English is spoken as the official  language in a huge number of countries around the word..  see  https://en.wikipedia.org/wiki/List_of_territorial_entities_where_English_is_an_official_language  ;

Each one of these places will most likely have their own English accent or more than one English accent.

Within England it is said there are more than 30 different Dialects or accents.    The USA also has a number of dIalect or accents within the Country.

Now I am from New Zealand and we have our own English accent.  We were originally colonized by the British so our base English was British English but since then we have had lots of immigrants from other English and non-English speaking countries and our accent has been influenced by that.  We also get a large amount of American TV so we tend to use many Americanism in our everyday speech. 

There are far more than one British accent or one American accent.  I'm pretty sure that in the other 18 or so countries there will be regional accents and none of those with be British or American.  Between Britain and America there is also a "mid-atlantic" accent which has developed from people travelling or appearing to travel between the two countries a great deal.

Most popular, who knows.  Hugh Grant seems to have a nice accent which is close to "Received English" a form of English used by many people in the UK.  Within the UK we have surveys on which accent is the most trustable and it tends to be a contest between Yorkshire and Welsh English.

There are more Americans than British, what accents do they like?

According to this article, https://en.wikipedia.org/wiki/List_of_countries_by_English-speaking_population, there are about 336 million people for whom English is their first language, with 231 million of these living in the U.S.   However, by the same article, there are more than a billion English speakers around the world when non-native speakers are included.  In my opinion, most of the non-natives I have heard do not really have either a clear American or a clear British accent, the largest number have a somewhat ¨international English¨ accent (a mix of different features)  with the most recognizable accent being the one from their first language.  

I tried to see if there was a survey about what accent people from different countries are focusing more on trying to sound like, because I have seen many people post here about their preference for one or the other-- finding one easier to imitate or finding one more pleasant to the ear. 

In my opinion, your accent is likely to end up sounding a bit closer to whatever accent you have the most exposure to-- if you have an American teacher and watch a lot of American TV your accent might end up sounding closer to American than British, or you might be the opposite with more exposure to a British accent.