Awesomeness is about shock and fear (of a respectful kind "awe") towards a particular thing or action. In this case, whatever you can possible find awesome in Anime is more so in other art forms.
The art itself is unrealistic, if you like abstract representations of reality, then any and all cartoon-styles would render equal "awe" but in reality no one finds art itself awesome, they find the artist's mind awesome or what the art is depicting awesome. The art itself can be pleasing but it is the creator and idea behind it which inspire awe.
As for the stories and themes anime hits that other cartoon styles don't such as rape and gore are indeed interesting at first but when we look at cartoons such as South Park and Family Guy, we see an intelligent way to go about inappropriate topics without actually needing to show much gore or vivid images to satisfy depraved pedophiles to legally view things such as "Loli porn" (one of many freaky subsects of 'Hentai').
What really is so awesome about anime? You think it's cool that they have fight scenes? Ever seen a real fight movie like Undisputed 3? I post a fight from Undisputed. The level of bodily mastery and directing requried for that fight surprasses the nonsense anime can offer.
Although anime is most of the time mistaken for henti it explores deep storylines that western films and shows don't even dare to enter. It teaches about friendship and curiosity but also explores deep sadness. ( I have cried so many times watching anime and I usually NEVER CRY!). It also teaches about perseverance, guilt,fear, and great life lessons to live by. A example I have is by the anime Ouran High School Host Club. (Mild spoilers). It's about a girl named Haruhi. Her family is middle class and she gets into wealthy Ouran Acadamy due to a scholarship. While she is there she goes into music room 3 and break the Host Clubs vase they were going to action off for 8,000,000 yen because she is middle class she can't afford to pay it off so has to work as a host to pay it off. Because earlier a kid in her apartment complex got gum stuck in her long hair she cut it all off to a pixie cut and looks like a boy. Because of this she make a great host. Charterers in this anime have dark pasts, great philosophy's, and even indirectly teaches kids about homosexuality and being Transvestite (this show was aired in 2007). It also teaches not to stereotype and to see what's on the inside of people. The most memorable line from the anime is a quote ( this was in the English dub.)by Haruhi that states (also before the quote they were talking abut her aperence and how she should dress like a girl.) "I just don't think it's all that important. Why should I care about aperences and labels anyway. I mean all that matters is what's on the inside right?" The show even teaches about not objectifying women and how friends have your back. Anime is one of those thing that you will be crying your tear ducts dry then 5 minutes later your laughing so hard your side hurts. Some whatch it for action but that's one of hundreds of genres. It's like saying that all tea is the same it's not. ( I would know I volenteer at a tea shop.) Anime is great because it teaches things western films and shows don't normally do. Like Sailor Moon for another example. Sailor Uranus and Sailor Neptune were both girls and Sailor Uranus dressed like a guy and had short short hair they were IN LOVE and it showed that affection on screen in 1994. Also anime explores universes that people never imaged. Like a notebook that can kill people. A land were Titans are the top of the food chain. A bunny cat young girls into selling there souls to fight witches when in the end they become them. And There is even anime for people who just want to see normal life like a anime about swimming with your friends or being in high school band. Anime is a place you wish that universe could exist in reality. You connect with charterers that deal with awful sorrow but smile the most. seam strong but even they have fears. Anime connects us when we live in a society that breaks us apart. That a fact!