How do you define "American comics"? Are you talking only about the superhero genre, or is fairytale stuff like Castle Waiting or coming-of-age stories like I Kill Giants also included?
It's an important definition to make, because "manga" is, really, all comics published in Japan - which is, I'm sure you'll agree, a wide range. It covers everything from gag-strips like 4Koma, up through the magical girl genre, sportsmanga, shounen adventure stories, and so on and so forth.
With this question, you're kind of asking us to tell you what we think of the way two entire countries' worth of comic artists handle the medium, which is really too big a question to answer properly. I'll do my best, though.
The mainstream of American comics - that is, superheroes from the Big Two - are not really my thing. There are a bunch of great comics published in the genre - I like Doctor Strange, for example, and DC's original 52 was pretty great reading, as is the new Hawkeye, and Ms Marvel, and so on - but as a whole, I find it hard to get into. There is just so much to read - so many decades of comics, under so many writers and artists and various character-incarnation, spread over so many different parallell universes - that I get lost and feel overwhelmed. I've got completionist tendencies - if I read something, I wanna read all of it - and the Big Two kind of make that impossible. There is not enough time for me to read it all, so I feel daunted.
But like I said - I enjoy some specific comics, for various reasons.
If we're talking the wider range of publishing in America, though, I am MUCH more positive. There are a BUNCH of great comics. The above-mentioned I Kill Giants, for example, is really amazing. Kelly-Sue Deconnick/Emma Rios' new project Pretty Deadly is, no lie, my pick for best comic 2014. Castle Waiting by Linda Medley is wonderful - and so on and so forth. I'm a huuuuge fan of Mike Mignola's Hellboy.
On the other hand, I love a bunch of different manga as well - Gokusen, Blade of the Immortal, Eyeshield 21, Yowamushi Pedal, Ran to Haiiro no Sekai, etc., etc. I really can't point to one nation and say I prefer their comics over the other - I just read a big bunch of everything, really. And that's not even counting all the European comics I read.
There are, of course, differences between the two - they spring from different cultures, after all. In terms of the actual craft of comics, there are noticeable differences. American comics tend to have a faster pace in the storytelling, using fewer pages to tell a certain sequence, whereas Japanese comics are more likely to allow slower-paced stories, with lots of silent establishing shots and mood/atmosphere taking up more space in the comics.
Then there is, of course, the use of colour. American comics - especially the more mainstream ones - tend to be full colour, whereas Japanese comics are mostly black and white. One isn't necessarily better than the other; they just give two very different impressions.
Another thing that Japanese comics do to a larger extent than American comics - at least up until recently - is contrast simpler, more abstracted figures against very detailed, realistic backgrounds. American comics have, in the past, tended towards the same level of realism in both figures and backgrounds. It's an interesting difference - and again, one is not necessarily better than the other. It's just two different styles of storytelling.
IMHO, there are American comics and cartoons with strong manga influences, but I personally only use the words manga+anime for stuff that is published in Japan - because to me, those terms denote Japanese-created things. Insisting on calling American-published stuff "manga" would be like me insisting on calling American/Japanese comics with Scandinavian influences "serier", because that's the Swedish word for comics.
But yes, there are certainly comics from both countries being influenced by one another.
