Disclaimer: I am not an accountant nor an employment lawyer.
Anti-disclaimer: I run a company in Spain, and pay people in other countries money to do things for the company.
My understanding is that in the EU your income tax, social security, etc, must be paid to the government in the country you are "tax resident" in. Typically, you are "tax resident" if you spend more than 180 days per year in a country. (Note: that doesn't mean that if you split your time equally between three countries you avoid being tax resident at all. If only avoiding tax was that easy...)
The company employing you _might_ be willing to help with the necessary headaches of abiding by the employment law of the country you are in. But they would more than likely prefer that you are self-employed/freelance/autonomous in the country you are in. Abiding by the employment law and tax law in your country of resident becomes your problem.
How exactly that works for your social benefits depends on the country in which you are tax resident. For example, here in Spain, a freelancer ("autónomo") is not automatically entitled to state unemployment benefits ("paro") if the work ends. But you are entitled to maternity leave and retirement pension. You'd need to talk to an accountant in your country to understand exactly how exactly being a freelancer affects your social welfare rights and responsibilities.
There certainly are some tax advantages to being a freelancer: eg. being a freelancer in Spain entitles you to claim a VAT refund on any business-related expense. That new computer you want to buy? Expect that in a year or so the tax department will refund you roughly 17% of the total purchase price (21/121 of the retail price).