first the fine print, then I'll answer your question
whether or not you're an employee or you're self employed is not really decided by you and your "employer", but rather by the facts of the case. You tend to be an employee and your wages subject to withholding taxes if you're paid hourly, if you have no risk of loss, if you work when and where and how your "employer" determines, if you have no other clients and if you otherwise do not conduct business like you're in business for yourself. You tend to be self employed if you have risk of loss, work for a contracted amount, you solicit similar work from other people and you otherwise conduct business like you have your own business. There are other variables.
There are ways to structure your relationship to minimize the chances of your relationship being reclassified under audit. Needless to say, many people simply ignore laws and do what they want anyway, and most never have any problem. The employer, not the employee, has more exposure when doing things improperly.
Now to answer your question.
the benefits/issues of being an employee.
1) employer pays 1/2 of social security and medicare taxes, 7.65% of gross. Self employed individuals pay all 15.3 % themselves.
2) employer pays for unemployment benefits and you can collect if layed off. Self-employed individuals cannot collect. This is extremely important if work is inconsistent or seasonal.
3) employer pays workers compensation insurance, so you can continue to get paid if you get hurt on the job. This is important in high risk industries.
4) you may be eligible to participate in employer benefit programs like health insurance of retirement plans.
the benefits/issues of being self employed
1) more take home pay initially, but this could be a red herring at the end of the day
2) it gives you an opportunity to deduct work related expenses, which could potentially save you tax dollars at the end of the day.
3) you should purchase your own liability and disability insurance (increased costs)
4) since the employer saves on payroll taxes, workers' compensation insurance, administrative costs and the expenses of any benefits he provides, you should ask him for more money. The employer saves at least 10%, and maybe even 30 to 40% depending on your industry, the state you live in and the benefits he provides. For example, workers' compensation insurance in the construction industry is 20+% in CT.
Needless to say, you need a good accountant if you're going to be self-employed.