If you're shopping for a DVD -- say, the first season of "Glee" -- would you find a better price at Amazon (AMZN) or Wal-Mart (WMT)?

Many of us would say Amazon, but Wal-Mart offered a better deal Friday on that DVD, both in its stores and on its website. Amazon charged $26.87 for the disc set, while Wal-Mart charged $24.96.

In fact, Wal-Mart beats Amazon time and time again on pricing, a study by research the firm Kantar Retail found. But Wal-Mart doesn't advertise this fact at all, and more of its customers are jumping to Amazon all the time.

Amazon has a well-deserved reputation for beating on price. Wal-Mart can compete tooth and nail at this level, however, because it has spent decades perfecting its warehousing, distribution and supply-chain management. It's also notorious for bullying manufacturers into rock-bottom prices.

Kantar compared prices on 36 items and found that Wal-Mart is about 20% cheaper, on average, Bloomberg reports. The difference was starker on food, where Amazon's prices were nearly 60% higher.

But Kantar looked at only 36 items. Amazon beats Wal-Mart on many, many others, and shoppers know that. Other studies have found Amazon to be lower than Wal-Mart, particularly because it doesn't charge sales tax in many states. Still, Wal-Mart seems to be competing more aggressively with its online rival.

Why doesn't Wal-Mart do more to advertise its price advantage? Why isn't Wal-Mart shouting from the rooftops, "Hey, all you Amazon shoppers, check us out for a change!"

It doesn't want to. "We'll leave it to Kantar to talk about prices," spokesman David Tovar told Bloomberg.

Meanwhile, more of Wal-Mart's customers are discovering Amazon. Only 25% of Wal-Mart's customers shopped at Amazon five years ago, Bloomberg reports, but that's now up to 50%.

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