Depreciation is the key factor here. A new car loses around 20-30% of its value in the first year, so if you buy a used one you avoid that brutal drop. In terms of pure price, a 2-3 year old car is usually much cheaper and will still be functional, especially if it has a good maintenance history. The trade-off is that it probably won't have a full factory warranty, though many dealerships offer limited warranties on used cars.
When it comes to maintenance, that's where things get a bit complicated. A new car comes with everything in pristine condition and no wear, so the first few years are generally cheap on repairs. But a well-maintained used car (and I'm saying this again, if you verify it has a good history) can be just as reliable. The important thing is to get a decent technical inspection before you buy it, don't just trust what the seller tells you. That can save you headaches later.
So, is it worth paying extra for a new one? It depends on how much money you have and how many years you plan to keep the car. If you're planning to keep it 10+ years, a used one at a good price is probably your best economic option. If you want peace of mind, a pristine car and don't mind spending more, go ahead with the new one. But honestly, most people regret having paid so much for a new car knowing they're going to lose so much money to depreciation the next year.