In the battle between Sprint (NYSE:S) and T-Mobile (NASDAQ:TMUS) for third place in the wireless phone business, one company has been the clear aggressor.

T-Mobile, led by its brash CEO John Legere, has never hesitated to mock its one-time potential merger partner -- or any of the other players in the field. The "Un-carrier's" CEO has made his feelings known at press conferences, to the media, and most blatantly on social media.

Ripping his rivals has been a big piece of Legere's way of doing business. For the most part, his counterparts have stayed above the fray. That changed recently when Sprint CEO Marcelo Claure took offense to a Legere tweet and fired back angrily on Twitter.

Source: Marcelo Claure's Twitter feed

It's a feisty move from Claure which shows that perhaps he's not wiling to simply cede the low-price, honest CEO market to Legere and T-Mobile.

What are they fighting about?
Legere's initial tweet attacked Sprint's All-In plan which offers a leased top-tier phone as well as unlimited high-speed data, talk, and text for $80. He did not specify why he feels the offer is a swing and a miss on Twitter and T-Mobile did not respond to a request for comment from GeekWire.

While he did not explain why he disliked All-In, Legere did take to Twitter to both tweak and compliment Claure.

Source: John Legere's Twitter feed

For his part, Claure not only got angry at Legere's comments, he used the social media site to post his own complaints about T-Mobile's marketing claims.

Source: Marcelo Claure's Twitter

Claure appeared to lose control a bit during his Twitter outburst, but he levels some pretty serious charges. T-Mobile has built its entire business around honesty, so attacking that is a major charge.

What will happen here?
While Claure has a point since T-Mobile's offer could be seen as confusing, it's likely that his attack on Legere was more a case of his showing that he won't be pushed around rather than an attempt to engage his rival over the long-term. It's unlikely that the normally upbeat, cool, and calm CEO will become a Legere clone. This was probably just a case of enough being enough.

Still, Claure's remarks proved a point. They showed that Sprint's CEO will stand up for his company and that he won't turn a blind eye to Legere as AT&T and Verizon generally do. That might give Legere pause in the future, though it's hard to think the hard-charging CEO will back off from a fight.

Still, while they may snap at each other a bit, both Legere and Claure know that the real battle is against their bigger rivals. Neither company will make huge gains stealing customers from each other, but the much bigger AT&T and Verizon look ripe for the picking.

This Twitter war showed that Claure has some fight in him, but he's likely to take the fight to the big boys -- not to Legere and T-Mobile.

Daniel Kline has no position in any stocks mentioned. He thinks Twitter Wars is a good idea for a TV show. The Motley Fool recommends Twitter and Verizon Communications. The Motley Fool owns shares of Twitter. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.