ARM is gunning for Intel by trying to break open the old-line PC and server markets. Meanwhile, Intel is charging ahead with new mobile offerings.

FORTUNE — Crack open your smartphone, and chances are there’s ARM—not Intel—inside. The British chip designer commands the mobile market. Last quarter alone, 1.1 billion of its power-efficient microprocessors were shipped in phones and tablets. But Cambridge-based ARM Holdings ARMH has bigger ambitions. In recent months, it has been talking up plans to get its chip designs into PCs and servers as well.

Meanwhile, Intel’s INTC been ramping up its efforts at penetrating the fast-growing mobile market. The world’s largest chipmaker owns the PC and server markets, but has failed to get its processors into smaller mobile devices. Recently, though, Intel scored several (albeit small) tablet wins. And it has said a phone powered by its Medfield processor will be unveiled by end of this year.

The two companies have long been on a collision course, but their battle for each other’s territory is about to heat up. By next year, Intel-running tablets and phones will have finally hit the market and ARM-based processors will have made their way into notebook computers (like those running Microsoft’s MSFT upcoming Windows 8). That will leave Intel breaking into a hot new sector just as ARM begins cracking open an old-line market.Of course, neither company is going to have an easy time taking on the other’s monopoly.

Intel has struggled to get a low-power processor into smartphones and tablets, but ARM executives are the first to admit they are worried about the encroaching competition. “You never discount Intel,” says Ian Drew, executive VP of marketing at ARM and a 14-year Intel veteran. “I’ve worked there long enough to know that they are a supreme manufacturing company.”

In addition to superior manufacturing capabilities, Intel’s size—whether measured in manpower or revenues—dwarfs ARM’s. Then again, ARM’s business model doesn’t require building multi-billion-dollar fabs. Unlike Intel, ARM doesn’t actually manufacture chips. Instead, it licenses its technology to companies like Qualcomm QCOM , Texas Instruments TXN and Nvidia NVDA and collects royalties on every device shipped with its architecture.

“ARM has great architecture and a lot of momentum behind them and Intel has superior manufacturing,” says UBS analyst Uche Orji. “Calling this one will be tough—the answer to this riddle won’t be clear until at least four to five years.”

In the meantime, predictions of who will grab what portion of market share are running rampant. Research firm IHS iSuppli recently said it projects that by 2015, 22.9% of notebook shipments worldwide will be ARM-based systems.

In the long run, the rivalry could be good news for consumer electronics manufacturers—and possibly even for consumers. Why? Because increasing competition among chip suppliers could eventually drive down prices. But it’s not clear either company will end up “winning” this match.

“I think they will both be successful to a limited extent,” says UBS’s Orji. “I expect to see some ARM PCs next year, and I also expect to see some Intel handsets in the market next year.”