When TomTom gave a gloomy update on its first-quarter sales expectations last night, shares of the European personal navigation device (PND) leader beat a quick retreat. They're down nearly 14% as of this writing. Other companies operating in GPS-related fields took collateral damage, including Garmin (NASDAQ:GRMN), whose shares slipped 7% -- apparently on the theory that what's bad news for one company is also bad for its archrival.

Yeah, I've never really gotten that logic myself. I mean, if consumers had discovered a sudden love of paper maps and were abandoning PNDs in droves, then what's bad for TomTom would also be bad for Garmin, Magellan, et al. But usually, if one company is doing badly, its biggest competitor is more likely than not doing better -- at least by comparison.

So let's test this thesis, why don't we? Just last week, Garmin issued an update on its prospects for its own current quarter. Now that TomTom has thrown its own two cents into the pot, today seems a perfect time to lay out the two companies side by side.

Let's start with Garmin. We learned last week that CFO Kevin Rauckman expects Q1 2008 sales to come in somewhere between $615 million and $738 million -- a 40% to 50% dropoff from the Christmas sales season but somewhere between a 25% and a 50% increase over the $492 million in product that Garmin moved in Q1 2007.

Contrast that with TomTom's news. TomTom blamed "retailers [who] reduced their inventory levels more strongly than expected" this quarter, and also its own decision to reduce "prices in the channel earlier than planned ahead of the introduction of new products in the second quarter," for the likelihood that Q1 sales will be "lower than in the first quarter of 2007."

How much lower? TomTom tells us to expect Q1 sales of 260 million and 270 million euros, "with an operating margin of a low single digit percentage." Translated, that makes for a 9% to 12% year-over-year sales decline to somewhere between $408 million and $424 million.

As bad as that sounds, TomTom's decline from last year's Q1 operating margin of 19% suggests to me an even steeper falloff in profits at the European GPS-maker. Though vague, TomTom's promise of "low single-digit" margins seems to promise at least an 85% slide in operating margin. Couple that with declining sales on which that margin will be earned, and scribbling a few back-of-the-envelope calculations, I think we could see TomTom's operating profit plummet as much as 90% or more when it reports earnings in two weeks.

Now, load on top of that the costs of litigating the European Competition Commission's challenge to its purchase of Tele Atlas, along with various non-operating expenses, and it doesn't take a whole lot of imagination to see TomTom booking a net loss this quarter. I'm not saying it will happen, mind you -- but after doing the math, I do believe it could happen.

Foolish takeaway
What I am saying, though, is that when you compare Garmin's news last week with TomTom's this week, Garmin looks to be the clear winner. We don't know what kinds of margins Garmin will produce, but we do know that its sales are growing as TomTom's are falling. Relatively speaking, therefore, I suspect that Garmin will come out on top in Q1.