An artist on deviantart posed the above interesting question on her journal.
My 2 cents:
It all boils down to personal drive.
I have met phenomenal artists from both sides of the fence ie. self-educated or attended an institute. I find that really, the background of an artist's education isn't correlated to future success, it's their initiative that is a bigger factor. Different levels of initiative require different forms of education.
So really, [money aside] the question of whether to attend an art institute or go solo is really determined in part by your personality.
If you feel you can scour forums, talk to peers, look at youtube tutorial videos, buy/lend out books and force yourself to practice to the point of self-loathing: Then you can be a candidate for self-education.
If you feel that having someone paid to keep the fire going under you and give you guidance and direction is crucial, then post-secondary art school may be for you. I find that the true worth of an art school isn't as much in it passing on technical skill, but rather in it teaching students to work under deadlines and the ever present shadow of outside expectations.
Now to bring a little middle ground to the discussion, I am self-taught, primarily through peer groups of artists, online resources, and lots of books. My Bachelor's degree was in Vertebrate Zoology and some minor studies in Molecular Microbiology, but I ended up getting a job in the videogame industry 8 years ago starting as a lacky background artist, eventually working to Art Director a few years later. I didn't have the financial resources or time to go back and study up in art school, so I decided to use an equally powerful source of education: Mentors and Peers. I attended local art school student meets/get-togethers and also signed up for late night figure drawing classes or any other courses that were offered.
I think that is an artist's "Ultimate Solution": Get yourself into a group of people who are of your skill level or higher, BUT make sure these people are more than willing to speak their mind about your art. You'd be surprised at how willing an artist is to go over their techniques if people showed genuine interest in their craft.
It's really a matter of whether you are willing to pay more money upfront, to gain quicker access to a group of peers/mentors, or you think you can already access these types of people and their knowledge by other means.
Addendum: It should be noted that having a post-secondary degree (in anything), may give prospective employers the impression that you can "buckle down and take instruction". This point loses strength as time goes by, and this is coming from someone who used to whittle down resumes based on academia alone. I find that a look through the portfolio, discussing their thought process and a general chat with the artist are better indicators of his/her potential than a degree ever will be.
On a compeltely different tangent, I have been spending my time doing backgrounds that can be tiled for a flash game. See below for an example: