There are two typical problems found in mainstream comics:  the common denominator reliance on old characters that have lost their edge and the overglorification of a comic franchise and its characters into a brand name. 
 
Let's take Wolverine and Superman as a prime example.  These two characters are probably the most popular comic book characters in mainstream media, so much that a fair percentage of people who know the names of those characters have probably never read a comic book.  They solely know what has been sold to them at the movies, on the shirts they wear, and in the product placement that those characters endorse.  It took a movie like X-Men Origins: Wolverine to actually let people know why Wolverine had this funky metal linked to his claws, as well as how he became who he became.  There's so much out there to absorb that the comics themselves seem like little more than source material to draw from in the eyes of the common person.  This overwhelming idea that they would have to read tons of comics in order to catch up to what the character is about and what he has been through can seem like a daunting and relatively time-consuming task. 
 
Superman happens to be the indestructible man, who's only weakness is to a green rock that made up his home planet of Krypton.  You could ask any given person where Superman is from, and again, a fair percentage of people wouldn't have any idea that he is even an alien.  Sure, you've got places to go for more of that information, like Smallville, but that origin may not be the same as the comics.  Stories may be diluted in order to become more friendly to another form of medium.  There's even people who could care less about Superman's written and illustrated adventures.  They solely care about that S logo.  They want the tattoo, they want the sticker on the back windshield of their car, and they want the backpacks and shirts and coffee mug.  They think they understand what that symbol stands for.  However, Superman in movie and TV form may be doing harm to the Superman mythos, and in turn, it may dilute the story of the comics to hopefully sell more copies to non-comic readers. 
 
Without independent comic companies, you lose a big point of comics: you are presenting story, mythos, and characters through a form of media that involves both reading and seeing.  In order to keep the big guys on their toes, you have to have the small guys that keep things interesting; offering new ideas to artists and writers who appreciate the work of their peers, if you will.  That's not to say that companies like DC and Marvel aren't capable of delivering a compelling story with interesting characters, but after a while, you have to decide whether you are interested in Wolverine the character or Wolverine the product, Superman the character or Superman the product.  When you pick up an independent comic, you are delving into a world of pure love, passion, and sure...the hopes that the creators can make a career and a little scratch off what they do.  However, the books you read from those independent companies will be a bit more daring.  They'll offer stories that you probably won't find in bigger comics.  You find yourself in a world of incredibly contrasted darks and lights.  The argument that makes independent comics a difficult choice for many to support is whether the products they offer are truly good or whether someone is simply being anti-corporate in supporting indies.  It's something you'll find in other forms of media, like movies and music.  Is something that is made independently truly better than something with a big budget behind it, as well as the advertising power to get millions of people onto it?  That is something that is up to the person making the argument themselves. 
 
In the end, I can't say that there is anything better about independent companies over mainstream, corporate companies...or vice versa.  There is simply passion.  Corporate workers like Jim Lee or Jeph Loeb are still as passionate about their work as any of the lesser known folks.  The only difference is that some get paid a million for their passion, while others scrape tooth and nail for even one reader.  In the end, without one, you can't have the other.  So long as you can keep the character and the product separate from one another enough to not corrupt the other, then who can truly complain? 
 
P.S. - Totally realize that the contest is over.  Just noticed that you could still comment and wanted to throw my two cents in.