First things first, make sure to check if you can actually rent the book you need. Some classes require access codes, and if this is the case, you can’t rent this book. You may also need a book for multiple semesters, and in this case buying the book would most likely be the cheapest option. Additionally, some books just don’t have the option to rent. I have seen some articles that state that the buyback programs for books can make up the difference between the rental and buy price, but this is usually not the case. You also won’t have that money until after you sell back the book, which means you could be in danger of cash flow problems.
From personal experience, renting is somewhat more difficult than just buying the books outright. Firstly, there are usually less places to rent than to buy. Secondly, you have to package it up and send it back to the company that you bought it from. It seems small, but it's one extra step. In general, renting your textbooks can save you a lot of money, but it comes with some additional tasks that you will have to keep track of.