You've forgotten the biggest difference. Joe has a car now, because the auto loan company has paid for it. Moe doesn't have one for 5 years, and how's he going to travel in that time? The dealer's not going to give him a car without the money.
This is why we borrow. I need the car now, maybe I need it to get to work, I can't wait 5 years and the only way is to be Joe.
It's even worse with houses. No way can I afford cash for a house so the only options are get a mortgage, rent, or be homeless.
To look at what financial advisers are getting at, let's say Joe and Moe both already have enough saved up for the car. So they're starting equal. Joe decides to keep his savings, get a loan and buy a car with that. Moe decides to buy a car with his savings. What happens?
Joe has to make repayments every month, and these include interest on the loan. Meanwhile he earns interest for 5 more years on the savings. Moe neither pays nor earns any interest on that amount as he's spent it. Now who is better off 5 years later?
I guarantee you that the interest rate the auto loan company charges will be more than what either of them can earn on savings. (It's one way banks make money. Get money in, lend it out for more, bank makes a profit.) Moe will no longer be earning interest on the amount of savings he withdrew to buy the car, Joe will, but he will also be paying out interest on the loan, and that will add up to more. And Moe can save for the next 5 years but Joe can't because he's spending that money on loan repayments.
Oh yes, it makes a difference! It's all about interest rates, which you failed to mention in the question.
On that sum of money each of them used to buy the car, Joe has paid out more money than Moe and will be worse off at the end.