I experienced all three forms of employment since I graduated from university four years ago:
- Employed at a company
- Working as an external consultant at a company
- Self employed as a contractor/freelancer
All three forms have their pros and cons. As an external I sometimes felt excluded and not being part of the company culture. On the other hand, I enjoyed the very few political meetings I was involved as an external employee. The salary as a freelancer is substantially higher due to the high hourly rates you can charge if you market successfully. But there again, is a downside: taxes and administration. You basically need to take care of all the book keeping, taxes, social insurances, retirement funds, etc. This tasks seem mundane at first, but they are very time consuming. Another point to consider as a self employed contractor is loneliness. If you're running into technical difficulties, you can't just walk over to your coworker and ask them for advice. Coworking spaces are mitigating this issue, but their working environment is way too distracting for me.
As you can see, all three forms come with different advantages and disadvantages. Overall, you should try out all of them and find out what works best for you.