Generally speaking, the most popular mangas and anime in the world are shonen. Naruto, One Piece, Bleach, Dragon Ball Z, all of these properties are the most iconic in the medium. When someone who isn't quite familiar with anime is asked to name one, they will generally land on one of those four as their example. It's not to say that shonen anime are the most popular among the anime-watching crowd, but it is these that find the most widespread appeal.
All of these properties are prime examples of Shonen Battle Manga. Shonen Battle Manga are basically exactly what they sound like; manga (and anime) centered around near-constant action-packed battles, with plenty of powerups in between these fights. Shonen battle manga are the most popular of the shonen genre, and arguably they make up the entirety of that genre.
However, there are still some popular properties that manage to circumvent or subvert (if slightly) the rigamarole of 'battle' manga.
I'm picking Shokugeki No Soma for my example here, mostly because I've been binge-reading the manga lately. Shokugeki No Soma is a recurring Shonen Jump title and has it's own anime adaptation as well. (Food Wars!)
It's undoubtedly a shonen manga, because of the high-school aged cast of characters and the plentiful amount of fanservice. The main demographic that the manga caters to is young adult men, same as Naruto or Bleach.
The main difference is that Shokugeki is a cooking manga, not a classic 'battle' manga. However, it does highlight it's own type of battling - the eponymous Shokugeki challenges of the series. In this way, two chefs compete head-to-head over agreed stakes in a bout of pride and energy. So it is a battle of sorts, but not in the traditional fisticuff sense.
It's this thought that raises a question; is it still a 'battle manga' even if the battling isn't the centerpiece of the work? Most websites I go to seem to list it as such, but I personally beleive that there should be a different kind of classification for it, and not just 'cooking manga' or 'sports manga' (like with PoT and Eyeshield). I think it only makes sense for there to be 'classic battle shonens' and maybe 'irregular battle shonens'.
But maybe I'm being too nitpicky.
Or am I?