This opening round features two of the world’s premier oil majors, Exxon Mobil Corporation (NYSE:XOM) and Chevron Corporation (NYSE:CVX). These are energy’s Duke and North Carolina, if you will.

Both of these oil majors are All-American dividend payers I’d love to have on my team. Exxon Mobil and Chevron have raised their dividends for 32 and 26 consecutive years, respectively, and both sport attractive current yields (3.2% and 4.1%, respectively).

But no tournament game can finish in a tie, so let’s take a look at both companies to see which energy titan is the better play.

Exxon Mobil (XOM)

Exxon Mobil has taken a beating of late due to the collapsing price of crude oil. Its share price is down about 19% from its highs last year, and for the first time in a long time, I can credibly say that XOM stock is cheap. Exxon’s dividend yield is the highest it’s been in decades, yet its dividend payout ratio is still very modest 36%.

I realize that the dividend payout ratio will probably spike in coming quarters as Exxon’s earnings slow thanks to the rout in crude oil prices. But coming from such low levels, investors have a wide margin of safety here. And XOM has a long history of maintaining and even raising its dividend under very difficult conditions in the energy markets. As I wrote late last year, Exxon continued to pay and raise its dividend throughout a 20-year bear market in energy. Dividend growth slowed a little … but surprisingly, not all that much.

It’s easy to keep your payout stable when your balance sheet is as rock-solid as Exxon’s. Its debt-to-equity ratio is a very modest 17%, and Exxon is one of only three companies in America to have its debt rated AAA by Standard & Poor’s. The other two are Microsoft Corporation (NASDAQ:MSFT) and Johnson & Johnson (NYSE:JNJ).

Exxon has also managed to maintain impressive profitability for an old-line behemoth from the 19th century. Its return on equity has averaged about 26% over the past 15 years.

Is there anything to worry about here?

Well, there is whole “Russia thing.” Despite the confrontation with the West over Ukraine, Exxon continued to invest heavily in Russian drilling rights throughout 2014. It now owns more than four times as much acreage in Russia than it does in the United States. For the foreseeable future, sanctions will prevent Exxon from doing much with those drilling rights, and they won’t do much for earnings. But Exxon appears to be taking the long view, betting that the deep freeze in relations will eventually thaw.

Now let’s look at the competition.

Chevron (CVX)

Chevron, like Exxon and the rest of the oil majors, has taken an absolute beating over the past year. CVX stock is down about 23% since late July and has underperformed the S&P 500 by nearly 28%.

As a value investor, there is a lot I like here. CVX is cheaper than XOM. Its price/earnings and price/book ratios are sitting near multiyear lows at 10 and 1.2, respectively, compared to 11.2 and 2.1 for Exxon. This is because Wall Street is a little less than enthusiastic about Chevron’s earning power in a low-crude-price environment … but after the beating CVX has taken, it would seem that the bad news is mostly priced in.

Chevron’s dividend yield, at 4.1%, also makes it one of the highest yielders in the S&P 500. And CVX has been a more aggressive dividend raiser over the past decade, growing its dividend at a 10.2% annualized rate compared to Exxon’s 9.6%.

To put that in perspective, had you bought Chevron stock 10 years ago and held until today, your effective dividend yield today on your original cost would be nearly 11%.

Chevron’s dividend payout ratio is a very manageable 42%. Even if Chevron shoots air balls for the next several quarters with new projects, its dividend would seem safe for the foreseeable future. Unfortunately, CVX recently suspended its share buyback program, which is a letdown but also a completely reasonable defensive move given its difficult operating environment.

Chevron has had a harder time ratcheting down its capital expenditures than some of its Big Oil peers, and this is unfortunately a pretty big deal. Several of Chevron’s big projects — including major liquefied natural gas projects in Angola and Australia and multiple platforms in the Gulf of Mexico — are at stages that require a lot of capital spending that cannot be postponed. That’s going to hurt profitability and may force Chevron to borrow more and crimp dividend growth. But with a debt-to-equity ratio of just 18%, Chevron has the ability to borrow pretty heavily without putting its long-term future at risk.

So, who is our winner here?

Our First-Round Pick: XOM

I’m going with Exxon. You take a slightly lower dividend today, but in XOM you have much better potential for dividend growth and continued share repurchases, and the Russian interests can be thought of as something like a call option.

If relations continue to deteriorate between Russia and the West, they expire worthless. But if Putin backs down — or is replaced — there is potentially a lot of value there.

Head back to the Stock Market Madness bracket to vote for your favorite stocks and check out other previews!

Charles Lewis Sizemore, CFA, is the chief investment officer of investment firm Sizemore Capital Management. As of this writing, he was long MSFT and XOM. Click here to receive his FREE weekly e-letter covering top market insights, trends, and the best stocks and ETFs to profit from today’s best global value plays.