Good question: it makes a BIG difference. When you purchase the car you claim the tax credit on your taxes, for however much you pay in federal income tax in the year of purchase (buy in 2016, file for credit the next year when doing 2016 tax return) up to $7500.
If you lease the car the tax credit goes to the leasing company. Here's where it gets complicated: the leasing company can, if they choose, give you the benefit of the tax credit by using it as part of the down payment or by increasing the residual value of the car. Tesla's leasing partner currently uses the latter method. By increasing the residual value of the car they reduce the capital cost that is being financed by the lease, thus reducing lease payments. However, if you were to buy the car at the end of the lease, Tesla's leasing partner currently charges the residual plus tax credit, meaning that you get zero benefit from the credit and the leasing company keeps it. This makes leasing-to-buy a very bad deal as Tesla leases are currently structured (but it could change).
Example: you lease a Model 3 for $42,000 and put $2000 down, the residual value at three years is $21,000. The lease would be based on $42,000 - $2000 -$21,000 = $19,000. So, your lease payments would need to cover $19,000 plus interest over three years. Counting the tax credit it would work like this:
$42,000 - $2000 - ($21,000 + $7500) = $40,000 - $28,500 = $11,500. The lease payments would cover $11,500 plus interest and be much lower than when they were based on $19,000.
So far, so good. However, if you buy the car off-lease you would pay $21,000 in the no tax credit case but would have to pay $28,500 in the tax credit case (according to Tesla representatives I have spoken with). The leasing company keeps the tax credit as pure profit, because they do own the car, after all, although it makes little sense if the goal is to sell cars.
Yes, I used that strategy when I purchased a LEAF in 2011: I converted a chunk of one of my IRAs to a Roth IRA, thus raising my income (because a taxable IRA to Roth IRA conversion is counted as taxable income). The problem is that by doing that I ended up raising my tax bracket, thus offsetting a large part of the benefit I gained from receiving the tax credit. (Because I ended up paying more in taxes than I would if I had just gradually converted my IRA over many years in a lower tax bracket, my usual strategy.) So, yes you can do this, but unless you stay in your usual tax bracket it is somewhat tax-inefficient. FWIW.
Just withdrawing money from a taxable IRA wouldn't work well unless you are over age 59½. Otherwise you would pay a penalty on top of the income taxes owed. Not a good idea.