The IRS W-4 is a document that determines how much income tax is withheld (not owed) from an employee's paycheck. IRS W-9 is a form that you give to people who will be reporting financial transactions they have had with you, so the correct Taxpayer Identification Number (TIN) can be associated with that transaction.
With that said, it appears that the question is asking about changing between W-2 (where taxes are withheld based on the W-4) and 1099 (where taxes are the responsibility of the payee) work.
There are significant differences between W-2 (employee) and 1099 (independent contractor) and you should be aware of all of them before making such a decision. To start with, whether you are classified as W-2 or 1099 is not solely at your discretion or that of your employer; the IRS has very strict rules about it and one or both parties may find themselves in serious trouble (generally, having to pay significant fines, penalties, and/or back taxes but I believe that criminal penalties may be possible though unlikely). See this link for help in determining whether you even qualify for this change. Understanding Employee vs. Contractor Designation
While an independent contractor can deduct many expenses that an employee cannot, the contractor will be responsible for self-employment tax at 7.65% (which is paid by the employer in W-2 work). Independent contractors are also not eligible to participate in 401k, do not qualify for paid leave (sick time, vacation, etc.), cannot typically participate in employer-sponsored health plans, and may not be able to enjoy many other perks provided by the employer. (Much of this might not be provided by a small employer, so the benefit may appear small.)
On the other side - the contractor can deduct the cost of doing business - tools and equipment used solely for the job, transportation costs (but not commuting costs), and other expenses. However, those costs may not add up to enough to make up the difference, particularly when taking into account the self-employment tax noted above. An independent contractor should also consider a number of other factors, including things like:
- short-term and long-term disability insurance
- liability insurance
- unemployment eligibility
- business-use vehicle insurance (your personal insurance may not cover this)
- mileage reimbursements (if provided by your employer)
There are sure to be many other small and large expenses that the average employee does not realize are handled by the employer.
Your employer may be happy to consider this change, since it may appear that he will be able to pay you the same (in absolute dollars given you) while dramatically cutting his own costs in the process; you should compute the correct hourly rate to cover your real expenses and determine whether this is actually acceptable to him or you.
Note that prior to 2018, employees who had significant unreimbursed expenses, and who itemized on their personal income tax returns, could deduct some of those expenses (that amount exceeding 2% of the adjusted gross). This deduction has been removed with passing of the The Tax Cut and Jobs Act; you may find that you benefit from the change.
My recommendation is to not make this change without fully understanding the ramifications; you may find it useful to consult a qualified tax professional to get assistance before acting on this idea. All other things being equal, you should at least be sure that you can deduct 7.5% of your income every year or you are sure to take an absolute loss. Don't forget the additional burden of bookkeeping and filing your taxes; your time is not free.