Generally speaking, unless you have very high vehicle expenses (expensive insurance, newest fanciest model), the standard mileage rate is more beneficial for most people.
Is this vehicle used 100% for self-employment or is it mixed personal and business use. That can significantly affect the deduction.
For the standard mileage method, you must know the miles driven for work and have good records to prove it. For the actual expense method, you must have the same records of work miles, plus you must have records for all your car expenses for the entire year (all your gas, repairs, maintenance, insurance) and your total miles driven for personal plus work. If you drove the car 40% for work, you deduct 40% of your car expenses, and that can include depreciation.
Special depreciation (if you are eligible) accelerates the depreciation -- you claim more up front but less in the future. You never depreciate the car more than it originally cost, you just change when. I don't know why claiming special depreciation would increase your tax owed, but one important fact is you can only claim special depreciation in the first year you place the car in service in the business. If you placed the car in service in a past year, you can't claim special depreciation now. And if you claim special depreciation now, you must always use the actual expense method and can't go back to the standard mileage method.
Also, since the standard mileage method includes an allowance for depreciation, but you don't have to make an adjustment when the car is older and depreciated, the standard mileage method gets you a bigger deduction over time if you are the kind of person who keeps their car more than 5 years.
And note, when you sell or trade in your work vehicle, claiming depreciation in the past may result in a taxable gain event when you sell or trade in.
You should read chapter 4 here first. There are implications to using the standard or actual expense method and some of the choices you make become permanent and can't be changed or revoked. https://www.irs.gov/pub/irs-pdf/p463.pdf
