The webcomic is the original. The manga is the adaptation of the webcomic, and the anime is based on the manga. The webcomic is noticeably further along. The anime, including the most recently aired episode from season 2, does not even put us at chapter 50 of the webcomic. The Garou arc ends in the webcomic at around Chapter 97, and currently extends to chapter 112.

The manga, however, begins to add a great deal more content not present in the webcomic at around the chapter 50 mark. The basic idea is still the same, but a lot of additional fights and sub-storylines get added.

So, yes, the manga is the more “fleshed out” version. ONE cooperates with creating (or at least approving) the new storylines and expanded backstories that appear in the manga, but Murata adds his own little take and spin on things in the end. My understanding is that everything in the manga can be considered canon at this point.

Some people prefer the one over the other, that said. There are two major points of contrast.

The webcomic has a crude simplicity to its art style. There are a few scenes here and there were you can see the mangaka actually does have greater artistic skills than you might otherwise have come to believe. This was the result of ONE originally not expecting it to take off in the way it did, and so approached it in a very relaxed style. Some feel it adds to the charm, and at times accentuates the comedy and certain character attitudes in ways a more refined artistic style perhaps could not. On the other hand, the manga is drawn by Murata, a highly skilled professional manga artist, capable of producing exquisitely detailed art. He approaches the task with a great deal of fun, often live-streaming as he draws new chapters. He was a fan of the webcomic who proposed the idea of him doing the art on a manga adaptation to ONE. Early in the manga there are scenes where he is clearly just reveling in the story and world and not worrying about forcing the story forward.
Pacing will be different. The manga version often drastically expands existing fights and backstories, or adds all new ones, while also introducing a whole host of additional monsters and heroes. The Boros fight in the webcomic is much shorter than it is in the manga, and Saitama never gets launched to the moon in the webcomic, for example. Some enjoy getting all of these extra details, while others may wish it would just move on to the next plot point. You can expect the manga will stay in this more heavily detailed but slightly more meandering style, as it is done in part to try to stop the manga from catching up to the webcomic too quickly (the webcomic has had multiple long hiatuses in its history, including one that only ended this month).