Ride-hailing, which involves booking transportation services via a smartphone app, is a two-horse race in the United States. Aside from legacy taxis, Uber Technologies (UBER -0.38%) and Lyft (LYFT 1.87%) are the dominant players. Uber is the market-share leader and an industry Goliath, while Lyft is a smaller competitor that might promise more upside as the underdog.

Which stock is the better investment today? It's a head-to-head you don't want to miss.

Uber's held onto its market share over time

Uber and Lyft are essentially the entire ride-hailing industry in America. Uber is the more popular service, and its name is somewhat synonymous with ride-hailing. In other words, you don't hail a ride; you call an Uber. Today, Uber holds roughly 75% of the U.S. market and has largely been able to defend that market share over the past seven years.

Lyft is competitive with the remaining quarter of the market, but the company hasn't expanded as well as Uber has. For example, Uber has become a global company, while Lyft is limited to North America. Additionally, Uber has branched out to food and package delivery, most notably via Uber Eats. Users can request package and food deliveries through Lyft, but it's much newer, having rolled out within the past year.

It's not that Lyft can't do what Uber can, but it feels like Lyft is chasing Uber's leadership in multiple ways. As an investor, I want an underdog to be a disruptor. If it's chasing instead, that can be a red flag that the business doesn't have a unique competitive advantage. You can see how this translates to growth below. Uber is growing faster than Lyft despite its much larger size:

UBER Revenue (Quarterly YoY Growth) Chart

UBER Revenue (Quarterly YoY Growth) data by YCharts

How profitable is each company?

The good news for both companies is Uber and Lyft are both financially rock solid. Uber is fully profitable, generating positive free cash flow and net income. While the business has over $9 billion in long-term debt, Uber is sitting on a whopping $5 billion in cash, and its trailing 12-month cash flow is $3.3 billion. That means Uber could rapidly shed most of that debt if it chose.

Lyft isn't yet profitable. The company has burned $248 million in cash over the past year. However, consider how much smaller Lyft is. The company is still growing to that magical point called operating leverage, where the business gets big enough that the economics of the business model shifts favorably.

That time could come soon; analysts are estimating Lyft will earn $0.63 per share this year. Additionally, Lyft has a comfortable $1.6 billion in cash on its balance sheet, more than its $865 in long-term debt. That means Lyft is rock-solid financially and shouldn't be going anywhere.

Which stock should investors buy?

Valuation is where things get interesting. It makes it hard to call a winner. Using consensus analyst estimates, Uber trades at a forward P/E ratio of 70 versus 26 for Lyft. Additionally, analysts expect annualized earnings growth of 52% (Uber) and 38% (Lyft) over the next three to five years.

I like using the PEG ratio, which compares a stock's valuation to the company's anticipated growth, to see how much an investor pays for that business' growth. I look for PEG ratios under 1.5, and both make it under that bar. Uber's PEG ratio of 1.3 is attractive, but Lyft's PEG of 0.7 signals the stock is an eye-popping bargain.

It seems the market is putting a hefty premium on Uber's stock for its market share and industry leadership. That's fair, but ignoring such a cheap stock valuation in Lyft is hard, especially as the company is turning profitable. Since I'm a long-term investor, I'd still have to give Uber stock the edge. However, seeing Lyft stock generate better short-term investment returns wouldn't surprise me.