Some of the pros are that you aren't pulled into company meetings and non-work-related tasks. You don't have a moonlighting clause and can work for as many customers as you want. You can negotiate provisions into the contract that you're interested in, like number of hours and contract length. You buy your own equipment and software and (most of the time) don't have to use the customer's old equipment. You schedule your own vacation and time-off (though it's polite to coordinate when you'll be on vacation). If you find yourself working with people you don't like, you can find another contract when this one is over and there isn't a job hopping penalty. You pick your own benefits.
Some cons, which might also be pros, are that you're running your own business and need to wear all of the hats. You manage your own payroll, buy your own supplies, and maintain your own benefits. You have to regularly find new work. You have to negotiate your own contracts and deal with customers who violate the terms. You do your own invoices and must ensure that the customer pays you. Sometimes, working through a recruiter can make some of this easier, but there are trade-offs where the recruiter wants to treat you like an employee too. You'll need to plan for gaps between work, meaning that you need to set aside funds in the business so that you can continue making payroll.
I've been independent for several years and it's worked out well for me. That said, everyone is different and it's good to get multiple opinions to compare with how it might fit your personal situation. I read books, talked to other people, and did a lot of research before taking the plunge.