Dullard did some specific math above, but keeping it simple, don't forget about the miracle of compounded interest. It might be cheaper, but with a higher interest rate, it's quite possible to pay more in the long run.
Also, something that I haven't seen a lot of people mention: if you have a very stable job that you expect to be at for a long time, then buying can be cheaper for a couple of reasons - most of the comparisons above only consider "now." In most markets, rent goes up over time; your mortgage payment is relatively fixed. (Taxes go up, insurance goes up, so with escrow, your payments may go up a little bit.) But, over time, perhaps even a decade, rent payments may very well go up beyond what your ten year old mortgage payment it.
E.g., if you have historical data for your area, see how much rent was 10 years ago, and see how much your mortgage payment would have been on a similar house 10 years ago. Your mortgage payment won't have changed significantly on a fixed rate mortgage - see how that compares to rents now that it's 10 years later.
And, the biggest thing: unless (like many people do) you keep deciding, "I can sell my house, put my equity into a downpayment on a new house, and afford a more expensive house." Then, after 15 years, or 20, or 30 - however long your mortgage is for, you're done. Just taxes, maintenance, and insurance after that. That is, if you buy when you're 25, then once you hit 55, you could be done making mortgage payments. How much is rent going to be 30 years from now? If you live to be 80, you can rent for 60 years, or pay a mortgage for 30 years or less. Of course, to do a perfect analysis of this, you would have to consider how much money the extra difference between mortgage and rent would be worth, with interest, until the point where the rent being more than the mortgage used up that excess.
Though, staying fixed to one house long term isn't for everyone. The alternative is moving laterally into another home at the same level in the market, rather than continually upgrading to bigger and bigger homes. But, a significant percentage of homeowners tend to always want to be in as much home as they can afford.