Self Publishing:
Pro: You have control of your work.
Cons: Total control of your work is a terrible idea if you don't know what the hell you're doing. Most neos don't.
The vast majority of self-published books go unnoticed and unsold--especially books by unknown writers with no professional sales.
The writer is out of pocket for all costs, including covers, editing, formating, interior design, etc. This includes writers who go to Publish America, which does not edit and overprices the books, making sales to the public nearly impossible.
Most of the time there is no distribution, which is essential to getting one's book in a store. Most stores will not stock vanity or POD books. Most libraries don't care to crowd their shelves with vanity and POD titles.
Unless you go with a place like Lulu, it can get bloody expensive.
Selling your book to a publisher:
Pros: YOU GET PAID.
Professional editing, covers, etc. free copies, reviews in Publisher's Weekly, DISTRIBUTION, foreign sales, you're welcomed into pro writing organizations like MWA, RWA, Writer's Guild, and get to sit at the tables with the cool people at events.
Cons: YOU GET PAID. Once you start selling words to a publishing house for real money, it's damned-near impossible to break the habit.