Editor's note: This post has been updated since it originally posted to reflect that Lyft is suing VanderZanden, not Uber. 

Lyft CEO Logan Green wants to make one thing very clear: His company is very different from Uber. Really,

Yes, technically, Lyft and its ride-hailing arch-rival Uber do the exact same thing: Provide smartphone apps that customers use to hail rides that are often cheaper or easier to find than a taxi.

But at a SXSW keynote Monday afternoon in Austin, Green tried to claim some bragging rights over his company's larger, better-funded rival. Namely, he said, Lyft is beating Uber at carpooling in San Francisco. 

"We have completely different visions of the world and we operate very differently," Green told an audience of about 2,500 people.

Within hours of each other last August, both Lyft and Uber introduced a new and very similar carpooling service, where riders who are heading in the same direction are matched together for a cheaper ride. Lyft's carpooling service, Lyft Line, accounted for the majority of rides in San Francisco as of the beginning of the year, Green said Monday.  

"We never set out to make a better taxi service. We want to make cars uneccessary," he said. He pointed out that Uber's original motto focused on the luxury and elitism of the service, whereas "we're relentlessly innovating to bring price down."

(It's worth noting that on the day Uber launched UberPool, its carpooling feature, the news arrived in a blog post with this line: "Since the early days of Uber, we’ve been excited about the idea of providing transportation so inexpensive and reliable, people can actually sell their cars.")

Green's speech is the latest skirmish between two close competitors, who have shared customers, drivers, executives and even lawsuits. It's widely known that drivers often work for both companies. And two separate legal cases argue that both companies need to start paying drivers as employees with benefits. (As independent contractors, currently drivers take on all the risks and costs associated with maintaining, fueling, and insuring their cars).

Lyft is also suing its former chief operating officer Travis VanderZanden, who left the company in August to go to Uber. Lyft alleges that VanderZanden, now head of international growth for Uber, brought his new employer confidential secrets involving Lyft's plan for growing overseas. 

On Monday, Green also emphasized Lyft's safety precautions, a point that Uber has come under fire for in recent months. Green said Lyft performs the most stringent background checks on drivers, including DMV records, as well as vehicle inspections. Uber pledged to strengthen its checks after a driver in India was accused of raping a woman who used the service.

(Citing unnamed sources familiar with Lyft's finances, Techcrunch reported shortly before Green's keynote that the company expects to make more than $1 billion in gross revenue in 2015 (but only $300 million net) but won't reach profitability until 2016.)

Of course, the average person hailing a Lyft or an Uber likely does not keep track of these tit for tats. 

Whether or not telling a better story can help Lyft beat out the much bigger Uber remains to be seen. The numbers suggest Lyft still has a steep climb. Uber has $5 billion in VC funding vs. Lyft's $850 million, and it's in 269 cities around the world, while Lyft is only in 65 U.S. cities.

Green told the SXSW audience Monday that Lyft doesn't have any international plans to announce yet, and he claims he's not worried about getting left behind abroad.

"We're absolutely learning a lot right now, watching Uber make mistakes abroad," he said.

Let the tit for tats continue.