It's a nice network, if you can get it, and you can get it if you try really, really hard.

Sprint is the only carrier selling an iPhone 5 with unlimited LTE data, which would be a great deal if anyone could actually get Sprint LTE. Only Atlanta, Baltimore, Dallas, Houston, Kansas City, San Antonio, Waco and a few much smaller cities have official Sprint LTE coverage right now, although the company promises more than 100 markets by the end of the year. Even in those markets, Sprint LTE coverage is slim, according to research firm Advanced Frequency Engineering.

Here's the thing, though: as Sprint turns on those markets tower by tower, iPhones suddenly become able to hit LTE. It's like they all get little jetpacks.

There is at least one live Sprint LTE tower in New York City right now. It's in the Bronx. I promised Sprint I wouldn't say more than that, but it's in the Bronx. 

When I walked into a quarter-mile radius of the LTE tower, my iPhone's download speeds increased by 21 times. That isn't unique to the iPhone, of course. The same thing happened on a Sprint Samsung Galaxy S III I was carrying.

Sprint's had a struggling 3G network for a few years now; in our nationwide tests earlier this year, we saw a poky average download speed of 410Kbps across our 30 cities. So the jump from that up to 12.3Mbps is pretty dramatic.

Back in June we tested Sprint's LTE in Atlanta before its official launch. This week's result was more impressive because it was on a real tower, out in the world, with phones connecting to it willy-nilly. It was a real-world experience.

Since I had both an iPhone 5 and a Galaxy S III, I tested them against each other on Sprint's LTE network. Across 20 tests, the Galaxy S III did better on 13 tries and the iPhone did better on 7, but really, the differences weren't enough to matter much.

Verizon Slow, AT&T Fast

Aside from the dazzling jump in speed on Sprint's LTE, the other shocker in my Bronx tests was how poorly Verizon's network did. I'm accustomed to a solid experience from Verizon LTE; it won our Fastest Mobile Network award this year because of its solid reliability and broad coverage. 

But in my 10 Bronx tests, Verizon just guttered. It dropped to 3G at three locations, which just shouldn't happen in New York City. LTE speeds were lower than both AT&T and Sprint, and 3G speeds were slower than Sprint's. I'm not saying this is representative, but it's a good notice that network conditions change neighborhood by neighborhood.

The winner? As I've seen before in New York City, AT&T's LTE blew away both Verizon and Sprint on speeds. Download speeds averaged over 19Mbps and I was happy to see upload speeds much faster than I'd seen before, at 10Mbps.

We Need More LTE

I'd love to believe Sprint's promises, except that we've been burned by Sprint 4G rollout promises before. Sprint's previous 4G WiMAX network missed deadline after deadline, got traded off to Clearwire and borrowed back, and has finally been declared a dead end. I really hope the company does better with LTE than it did with WiMAX.

Right now, for the three biggest carriers, the race towards mobile Internet is all about laying down LTE. Sprint and Verizon have relatively slow 3G systems; AT&T uses a faster 3G technology, but its network is terribly congested. The great speeds on Sprint LTE simply show that Sprint needs a lot more LTE, as soon as possible.

For more, see PCMag's review of the iPhone 5 (on AT&T) and the slideshow below, and our review of the Sprint Galaxy S III.