Sadly for Apple’s domestic partner, AT&T, the first round in a legal battle with Verizon Wireless over their “There’s a map for that” ads is a defeat. A Federal judge in Atlanta declined to grant AT&T a temporary restraining order in an effort to force Verizon to stop showing the ads.

The series of ads almost appear aimed directly at the complaints of iPhone users against AT&T, showing two maps of the United States with seemingly poor 3G coverage in blue from AT&T, while the majority of the country is blanketed in red showing coverage from Verizon.

AT&T responded with a lawsuit in Federal district court earlier this month, going on the offensive in an effort to paint the Verizon ads as misleading. According to AT&T, the ads imply that mobile phone users outside of the blue areas won’t have any data or voice coverage at all. They don’t dispute the validity of the map’s depiction of the actual 3G coverage, but the reality is that any connection made outside of the blue 3G area will use the company’s slower EDGE or GPRS network.

For their part, they suggest that the advertisements simply point out that AT&T is not investing enough in upgrading its network to handle the increase in traffic from data-hungry smartphones like the iPhone. At any rate, Verizon has tweaked their ads slightly to make it clear they are referring to 3G coverage and not the slower 2.5G service. Verizon claims five times more 3G coverage, which their maps seem to bear out.

“While we are disappointed with the court’s decision on our request for a temporary restraining order,” says AT&T spokesman Mark Siegel, “we still feel strongly that Verizon’s ads mislead customers into thinking that AT&T doesn’t offer wireless service in large portions of the country, which is clearly not the case.”

In a sweeping 53-page rebuttal to the court earlier this week, Verizon claimed that AT&T is not suing because the claims are false, but because it doesn’t want to face the truth about its network.