Alright, I think it's easier for me to break down the characters I like into four distinct groups:
Characters in a Great Story: So, maybe I like these guys more for the story they're in. All-Star Superman, Cloud 9, Adrian Veidt, Rorschach, Cable(Cable & Deadpool)
Like them Because They are Jerks: It is a shitty reason, though I worked really hard to come up with that 'righteous violence' thing, which I stand by, but it is just a fancy way of saying “I like a character because they are a jerk and I'm just going to go ahead and act like it's actually a call-out to the fundamental nature of the medium.” Midnighter, Ultimate Captain America, Damian Wayne.
Fun to Read: What it says. Also the previous group should probably be included in this one. Booster Gold, Deadpool (Cable & Deadpool)
Icons: Batman, Jenny Sparks
What sets Jenny Sparks apart from, say Adrian Veidt? Narratively speaking, they're very similar. In fact, they have a lot in common: both want to save the world, both have leadership abilities, neither one really wears a mask, both have bad-ass hideouts (not like that's uncommon in comic books. Hell, it was once so common that it became chic not to have one. Now, unless you're Batman, you only have a cool hideout if you've paid your Save-The-World dues or if you have it ironically.), both are liberal (possibly homosexual), and both really just have one badass story arc that left a massive impact on me.
So what is the difference? Jenny clearly has more color; she yells and threatens and smokes and has regrets and is even proud of herself in a way that expresses her doubts. The recap we've gotten of her life is someone whose idealism has destroyed her and who has learned to believe again. Adrian Veidt is a singular character who starts out determined and idealistic, and who retains those two attributes despite so much opposition and cynism, and even defeat. He does make the world a better place in the end (which Jenny doesn't actually do; she just saves it and gives her people a good push in the right direction [which they use to make themselves an object lesson in why, if you want to be aggressive about changing the world you use a psychic squid or some shit instead of punching things]), but as amazing as the book is, Veidt's rescue isn't an entertaining read.
Watchmen uses its prodigious size to convey a setting, set up an idea, and draw believable characters who support those two things. While I can read through it over and over and pick up new, minute details that keep it fresh for me, it does lose something whenever you know Veidt “did it” thirty-five minutes ago. It (and by the extension, the characters in it) is a good book with a distinctive feel and great ideas behind it. Watchmen is a deconstruction of the superhero genre, but deconstruction can mean many things. Traditionally, when it's used with respect to literature, it refers to the reduction of a subject to base components whose inherent contradictions are revealed. I believe this is the meaning most use when they talk about Watchmen, but deconstruction can also refer to a simple analysis by examination of base components. I believe this is what Watchmen is better at; distilling various elemental pieces of the superhero genre, but in doing so, it loses the fusion that gives a superhero book its spark. It isn't viscerally exciting. You aren't enjoying yourself when you read it; you're thinking about what its saying and appreciating the finely crafted mesh of this tiny world and how all its pieces are gratuitously woven together.
The Authority (and even Stormwatch), is fun to read. It's bombastic high adventure, superheroes doing what superheroes do best. There's only a little pretense here and there, and the character development is done as the protagonists are solving (punching) the problem at hand (or not, in The Doctor's case).
So the heroes I like are the ones that have moments or stories I viscerally enjoy reading. They either have (or promise to have) “that time” moments, like that time Jenny had The Authority stop a superhuman army from leveling London. Or that time that she stopped an alternate universe invasion of Los Angeles by electrifying most of the invading fleet, broadcasting a warning with her own powers that they never return. Ultimate Captain America has exhortations about abbreviating the names of countries, The Midnighter gets to shatter people's will with words, perforate baddies with jackhammers, and ram small island nations with shift-ships, Booster Gold has...well, one time...alright, Booster doesn't have Crowning Moments of Awesome, he would have Dethroning Moments of Suck, but really, Booster never gets high enough to be dethroned from anything (until some family-member-turned-evil in a mask bursts through his bathroom wall one morning). Damian...well, honestly his most memorable moment was trying to take a crowbar to The Joker and getting poisoned, captured, and then delivered to Simon Hurt as a pawn in The Joker's game of revenge against Hurt and his Black Glove(Update: There was totally this time in “Teen Titans” where there this kid ripping up a place with superpowers. Raven takes him to a pocket dimension to calm him down and convince him that the Titans want to talk to him. The minute he returns to the real world, Damian just clocks him with a full-body sucker-punch the likes of which only a ten year old asshat could deliver.).
Next All Previous