Claiming “irreparable harm,” AT&T (T) has filed its second lawsuit in two weeks asking a U.S. District judge to force Verizon (VZ) to pull its new TV ads — cartoons that depict the iPhone as the latest arrival to the “island of misfit toys.” The issue, once again: coverage maps that AT&T claims are “false” and “misleading.”

On Thursday, AT&T followed up with a “set the record straight” letter reminding customers and the press that it, not Verizon, carries the “most popular smartphones” — i.e. Apple’s (AAPL) iPhone — and that its customers, not Verizon’s, have access to more than 100,000 applications.

The letter includes a link to the version of AT&T’s coverage map — shown above — that the company thinks Verizon should be showing in its ads.

We’re not so sure. Let’s look a little closer at this map — and some others — below the fold.

Here are the two that triggered the lawsuits. They show Verizon’s 3G coverage (red) next to AT&T’s 3G coverage (blue).

AT&T takes strong and litigious objection to this comparison because, in the words of its lawyers, all that white space in the right-hand map “falsely communicates that AT&T does not have wireless data coverage throughout much of the United States.” (Full text of the complaint is available here.)

According to AT&T, its wireless network actually reaches 303 million Americans — 97% of the population — if you include 3G, EDGE and GPRS. That’s how they can justify drawing a map in which most of the country is painted blue.

But is that fair? AT&T’s 3G service, when it works, is zippy enough. But EDGE (a 2.5G service) is considerably slower, and GPRS (2G) is slower still. A more accurate AT&T map would distinguish among the three services. You can get that from AT&T here, but it takes some effort (and a Photoshop session) to get one map that shows the entire lower 48 states. When the work is done, this is what it looks like:

Like Verizon’s map, this one displays AT&T’s 3G coverage in blue. And in fact, the correspondence between Verizon’s blue splotches and AT&T’s is pretty good.

But even that is somewhat misleading. If you drill down into AT&T’s map of densely populated cities — say San Francisco and New York — you get the impression that the two metropolitan areas are swathed in 3G blue. See below:

But as anyone who relies on an iPhone in those cities can tell you, there are times of the day when an accurate map would look more like blue Swiss cheese, with big white holes in the business districts where you can’t data or phone service.

If, as rumored, Verizon may be getting the iPhone in the next year or two, these maps — and those white holes — could mark the battle lines for a long drawn out war.

See also:

• Verizon vs. AT&T: There’s a map for that
• Rumors: A Verizon iPhone in 2010
• AT&T Mobility is nipping at Verizon’s heels

[Follow Philip Elmer-DeWitt on Twitter @philiped]