Most of the time, this is a purely theoretical question. After all, how many of us get to choose whether a position is independent contracting or employment? Companies usually make those decisions long before we get a chance to apply for a job.
However, understanding the pros and cons of employment and self-employment can help you make apples-to-apples comparisons between different positions. Or, understand what a change in status might mean for your paycheck.
Last year, a client for whom I worked as an independent contractor ask me to change to employment status. Since the client didn't want to change my freedom to schedule my time or (gasp!) make me work in an office but was now going to pay half my Social Security and Medicare tax, it was clearly a good thing for me. But sometimes it's not always that clear cut.
To help you sort out what might be better in your case, see these articles: