More generally, it's hard to find equivalents between popular (imported) anime and (domestic) notanime genres. Action/adventure shonen only vaguely resembles action movies or most actionish cartoons; superhero stuff is probably its closest relative.
This is honestly one of the biggest reasons I watch anime right here. The drawn medium means that I can get characters whipping out superpowers and duking it out in awesome, glorious battles fairly regularly throughout a show like Unlimited Budget Works. The quality of the fights might differ a fair bit from show to show depending on the budget, but at the basest level I can still get things like fire flinging that at least look ok. On top of this then I can get a mature story that actually focuses on serious challenges and questions, or on the character beating overwhelming odds.
Here's my alternatives in the US:
1) Live action superhero films (like the Avengers, etc.). I watch these... pretty much all of them. But when you only get about 8 hours of entertainment out of this number every year, it doesn't exactly take up a lot of my time.
2) Live action superhero tv shows. Ever notice how these seem to give everyone awesome powers, and then go quite a bit out of their way to
never actually use them? This is because live action special effects cost through the nose. If that character can control fire, then I don't want their total power usage in the series to consist of lighting candles and throwing a fireball once... in the show opener. If you are going to give a character powers that can use a power to solve problems, then you shouldn't be hitting them with the idiot ball every time their powers could solve a problem, which superhero tv shows do pretty often because they don't have the budget to actually do special effects that match the world they need to exist in.
3) Animated superhero tv shows. These tend to boil down to either "never really challenged hero beats up bad guys who have no real hope of winning every week" or "weekly moral because we couldn't have done this without the power of trusting our friends!" There are a few things that tend to avert that somewhat (parts of Teen Titans, Young Justice), but once again it's the same problem as #1, there isn't exactly a whole lot of content being generated.
In contrast with anime I can get something that looks good due to all the clean lines, actually busts out character superpowers for plot solutions and awesome battles on a fairly regular basis, and still approximates more of a story than "So you see Johnny, don't litter, because then superpowered mutants from the sewers will rise up to destroy the city. Recycle instead, and you too can be a hero!". And sure, a fair number of those superpower shows throw in haremshit, etc., but honestly, as long as it's got a cool enough battles and intelligent use of powers, then I could care less if they occasionally delve into things that aren't as good.
Finally continued watching Puella Magi Madoka Magica. I was on episode 3.
Dear god.
Heh. Heheheh. HEHEHEHEHEHEHEHEHEHE.