Last summer, the Netflix (NFLX) CEO tried to introduce a new fee structure that most subscribers viewed as a price increase. A few months later, Redbox raised its DVD rental fees by 20%. But Redbox customers gave it a pass. The level of grumbling was nothing close to the hostile revolt Netflix endured.

But here’s the thing. Netflix’s fee change reflected the costs of running both a DVD-by-mail business and a growing library of streaming titles. Under the new subscription fees, the monthly fee for a DVD-only subscription went down to $7.99 a month from $9.99. Redbox, which has no streaming service, raised its rental fees from $1 a night to $1.20. But if anything, it seems angry Netflix customers are flocking to Redbox.

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This week, Redbox parent Coinstar (CSTR) reported its earnings for the first quarter of its higher fees. The results far surpassed investor expectations: $1 a share in earnings, against analysts’ estimate of 65 cents. Coinstar’s stock, which surged 14% the next day alone, is now 36% above where it was a year ago. And Netflix? It’s down 43%.

Redbox began a decade ago as a McDonald’s-sponsored (MCD) experiment with kiosks selling milk, eggs, pantyhose and DVDs. In time, the kiosks sold only movies and by 2009, when Coinstar bought out McDonald’s remaining stake, revenue was above $400 million. Even then, Coinstar was seen more as a place to dump pocket change than as a rival to Netflix.

For much of the past year, however, Redbox has succeeded by being the anti-Netflix. While Netflix has strived to move beyond the DVD-rental business, Redbox, which controls 37% of that market, is moving more deeply into it. Its kiosks, fixtures in the front of Wal-Mart (WMT) and Walgreens (WAG) stores, is expanding to new chains like Safeway (SWY). This week, the company said it will buy the DVD-kiosk operations of NCR Corp. (NCR) for $100 million, boosting market share to 42%.

That counter-intuitive bet is working so far. Redbox — which makes up 85% of Coinstar’s revenue — saw its revenue grow 35% last year to $1.6 billion, slightly less than half of Netflix’s 2011 figure. Redbox’s operating profit grow an even healthier 48%; Netflix’s grew 36%.

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Redbox raised its DVD rental fees without spurring a Netflix-like backlash by pitching it as a necessary move in the face of new government regulations on debit-fee transactions. In trying to reform debit-transaction fees, the Dodd-Frank Act ended up raising fees on low-cost transactions like $1 DVD rentals. And in contrast to the furor over Netflix fees, the increase seemed modest.

But Redbox raised fees much higher than it needed to account for higher debit-transaction costs. An analyst at D.A. Davison said Dodd-Frank would increase rental costs by 5 cents. The other 15 cents Redbox made went to the company itself.

The next few years are likely to be tougher ones for Redbox. If Redbox is looking more like Netflix, it is the Netflix of several years ago — a company dependent on rentals of DVDs, a dying business model, and in need of streaming-video licensing deals that could eat into its profits.

To address that, Coinstar signed a joint venture with Verizon (VZ) offer a subscription service combining Redbox’s DVDs with digital offerings. Details on the joint venture are sparse so far, but it’s expected to launch later this year. Redbox will own 35% of the venture, and contribute an initial $14 million, and perhaps much more over time.

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The deal will give Redbox exposure to the streaming-video business that is the heart of Netflix’s business today. But it will require Redbox to, like Netflix, negotiate with the big studios — some of them the same ones that the company has exchanged lawsuits with over DVD licenses. Redbox and Warner Brothers recently declined to renew a DVD agreement. (Warner Brothers is owned by Fortune‘s parent company.)

Charlie Wolf, an analyst at Needham & Co., doubted that Verizon and Coinstar could gain traction in licensing content. “Unless Verizon and Coinstar are prepared to spend an amount that’s in the ballpark with Netflix and/or possibly Amazon (AMZN), the service is unlikely to capture a material number of households” Wolf wrote in a report. For now, Rebox’s momentum is helping it setup a confrontation with the bigger Netflix. But there’s no doubt that that momentum is the product of a good 2011 built mostly on a business of the past.