Make no mistake. This is no friendly competition. When it comes to the battle for wireless subscribers, Verizon Wireless and Dallas-based AT&T are in an all-out war.

For the past several years, AT&T has been seeing its exclusive contract with Apple pay dividends, with lucrative iPhone customers now making up an estimated 26 percent of its post-paid subscriber base. Verizon, meanwhile, has been pumping billions into its wireless infrastructure.

It’s gotten to the point where AT&T is a whopping $5 billion behind Verizon Wireless in the race to build America’s best wireless network, according to an independent research firm that studies the telecom industry.

Littleton, Colorado-based TownHall Investment Research says AT&T’s wireless business faces threats on several fronts, including the expensive need to link its wireline network to its wireless network and the potential end of its exclusive iPhone contract with Apple.

First on the fix-it list, though, according to TownHall, is wireless connectivity and reliability. “The wireless network quality has been the elephant in the room for AT&T,” said Gerard Hallaren, director of research at TownHall. “I think it’s a major issue for them.”

According to TownHall’s research, between January 2006 and September 2009, AT&T spent about $21.6 billion, or $308 per subscriber, on its wireless network. During that same period, Verizon Wireless spent about $25.4 billion, or nearly $353 per subscriber.

In addition to covering the $3.8 billion gap in wireless-network spending over the past three years, Hallaren said, AT&T will have to spend an additional $1.2 billion to handle future traffic demands.

An AT&T spokeswoman, McCall Butler, declined to comment on TownHall’s capital-expenditure figures, but said the research is based on incomplete information.

“They don’t provide a complete picture of AT&T’s significant investment to support our mobile broadband leadership,” she said. “Overall, we think our network performs really well.”