The only problem with manga style comics is... ok again I lied, you know there's always more than one problem with most things.

The main problem is that the art style is more unrealistic than American comic book style, proportion-wise. You either love it or you hate it.

I like it but I wouldn't say I love it.
It's slightly easier to copy that style than American style.
To clarify, I will call the superhero comic book classic style that we all know (e.g DC, Marvel, Dark Horse etc) American style here, just for quick differentiation.
I know that in America and Japan they have more than one drawing style, and anyone can draw in different styles but the mainstream styles are what I'm talking about. I also know that you can get manga style comics from China, Taiwan, Korea and other countries but include those in Manga style. Ok?
Most western Manga style comics are not drawn correctly. They are done too cartoony and blocky and do not have the same feel at all. Usually done by people who want to jump on the Manga bandwagon and make some money. However some of us who have an eye for good lines and curves, can tell the difference immediately. Some western Manga are not bad. But most, suck, frankly. They are poor copies of something good. Even their stories and dialogue are childishly lacking in nuance (subtle quality) or originality.
I hate giving Manga a capital. So lower case here we go.

Weaknesses for manga?
Overly emotional and sometimes goes more dark than American.
Sometimes really dark... torture, rape, gore, incest, pedophilia. I have to be very careful what manga I get into. It's such a mess sometimes.
Less attention to movement, more to backgrounds, beauty and emotional expression.
Sometimes too dramatic, and sometimes too weird, e.g stuff gets lost in translation... your sense of humor may vary...
Slow to build up action sometimes. This can make a story a downer or boring.
The EYES... too big!
Ridculous hair! and some ridiculous heroes, it's hard for me to believe in a story if the characters are too over the top ridiculous in appearance or their powers or how they talk. I don't feel a connection, it doesn't feel real enough and so I have no sympathy or interest in them. Maybe because I'm not Japanese I have this problem, I don't know.
Cheesy too, sometimes. Esp shonen (manga for boys). 'You're my rival! YOU CAN'T LOSE, PROMISE ME!!!' *amazing amount of crying*
Why is there almost always a pervert?
Why is there almost always a main character who is an IDIOT???
Why are girl's boob sizes so important????
So much magic....
So much ridiculous levelling up! And new powers and abilities being discovered.
Dying is not always permanent, but they don't do that quite as much as the American ones do. Although that's only because modern manga which is becoming like Asian mutant (they never call it that though) superhero madness (copying you-know-who), is younger than American comics, so they haven't had superhero (sorry don't know what Japan would call it) characters running in comics for literally decades yet. But they are close!
Art getting better, more fluid, colourful etc, but most characters becoming cliques of older ideas that were done better and more meaningfully. Basically the better the art, the worse the story seems to be, these days. A few exceptions but generally, my catchphrase is, 'Oh yeah, that's like .... and I liked .... better. Oh, you don't know what .... is? Google it. Watch it or read it. I promise you it's way better.'
Manga adaption to anime is often bad, depending on what studio takes up the story and how many episodes they are prepared to do. They ruined Ouran High School Host Club, in the anime. Sorry but the manga was MILES better.
Sometimes hard to tell characters apart. But that's the same as American style.

Strengths:
So different.
Sailor Moon. Ranma. The 90's stuff was good, art was improving, becoming more ambitious, yet retaining good characters and interesting plotlines. It was all new.
Novels become manga become anime (aka animation, cartoons). Or even better, live drama. And can become a game or several games! Awesome.
Beauty. Style, grace, intelligent dialogue (sometimes haha). The hero isn't American. Or always a male. Or even human! It doesn't matter. They stories are good, lots of plot twists but not so stupidly complicated that people give up.
Not always a perfectly happy ending or a stereotypical ending. Slam Dunk, for example. Oops, spoiler alert. On the other hand, at least most manga have an end in sight. American comics....when will it all end satisfactorily? Nobody knows.
Black and white is usually enough. I don't need colour, the drawings are good enough to see what's going on. Usually...
Amazingly diverse stories, and characters (usually). Interestingly diverse powers or skills. Lots of humor. Clever stories sometimes. Thrillers, mysteries, sci fi, fantasy, magic, everything. They can take any idea movie or story and turn it into manga. They did it with Star Trek, and the Labyrinth, and likely many others.
Attention to detail, clothes, water, backgrounds. Even a table.
Interesting characters than you can relate to, and you end up caring about so many, not just the hero.
Anywayyy at the end of the say it's all a matter of taste.

Whether you think American style  is better than manga style.
I like both. Sometimes you don't need to choose. You can enjoy everything.
To be clear, I am not saying one is better than the other.
I'm just listing likes and dislikes, which is something I like to do.