Money is a surprisingly good proxy for energy and carbon impact. If it's cheaper to buy than rent, then it probably uses less energy too.

When you rent a car, it has to sit in the rental car parking lot. They have to build the facility. An employee has to drive there to do all your paperwork and rent it to you. The rental gets fully cleaned and inspected after a day of use by another set of employees. They all have to eat to work and a lot of energy is used to produce that food. All of this and more is encapsulated in the price.