The major manhwa companies often mentioned are LINE Webtoon, which has a huge fan base, and Tappytoon, which is known for its quality releases. Also, Mr. Blue is gaining popularity for its interesting manhwa offerings.
I'd recommend 'Champion's Path'. It's similar in that it showcases the protagonist's journey in the fighting arena, facing various challenges and opponents, much like in 'The Boxer'. The character development and plot progression have some similarities too.
It's hard to say which is better. Manga typically offers more classic and well-established franchises. However, manhwa has been gaining popularity for its fresh takes and innovative concepts. It really comes down to what kind of stories and art styles you prefer.