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If you want to add a high-dividend energy stock to your portfolio, there's rarely been a more opportune time to consider Chevron (CVX) - Get Chevron Corporation Report or Exxon Mobil (XOM) - Get Exxon Mobil Corporation Report . With energy prices at depressed levels, their shares are trading at bargain levels. But which is best for income?

Exxon Mobil has a market capitalization of $346 billion, twice that of Chevron's  $168 billion. But Chevron promises super growth, while stability is Exxon's forte. Let's examine their respective strengths.

In terms of stock price movement, it's Chevron that's made much more progress in the past month. Chevron's stock has gained 18% compared to Exxon's 13% gain:

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CVX data by YCharts

Even after those gains, however, Chevron is down 20% year to date as opposed to Exxon's more modest 11.6% decline:

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CVX data by YCharts

On a five-year basis, Chevron has inched up by 9% while Exxon gained 24% in the same period:

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CVX data by YCharts

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Chevron may be a little ahead of Exxon in recent times, but for the long haul, the latter has made investors richer in terms of stock price appreciation.

Both stocks offer solid dividends. Exxon has a dividend yield of 3.45% while Chevron has one of 4.76%. This is where we take out our calculators and use the total return metric (which takes price appreciation and income into account) for a closer analysis. Exxon beats Chevron, albeit narrowly.

For the one-year, three-year and five-year periods, Chevron has exhibited total returns of -19.61%, -2.80% and +5.61%, respectively. On the other hand, Exxon has racked up -10.06%, -0.19% and +7.17% over the same periods. Keep in mind that this is all based on trailing returns.

Profit margins for both businesses are similar at around 8%. In terms of debt, both oil companies have around the same levels, though Chevron packs more muscle in terms of cash, when compared to Exxon.

Let's look at how the future earnings scenario stacks up. If Exxon's one-year  earnings estimates are taken into account, the oil major trades with a forward price-to-earnings ratio of 20.25. Chevron trades at a forward P/E of 21.66, at a slight premium to Exxon. In 2016, Chevron is projected to grow its EPS by 30.1%, while Exxon is expected to see a slower pace of 5.2%.

This is why we think Chevron has an edge over Exxon, in terms of valuation. Overall, you should beware of "value traps" in the energy patch. Case in point: Chesapeake Energy is now down 64.5% year to date, but we would never recommend buying this essentially doomed stock just because it's cheap.

Higher earnings should logically be a precursor to better stock price movement or higher dividends or both. Now which stock is more capable of sustaining dividends?

A good way to figure this out is to look at dividend as a portion of free cash flow. Chevron in the trailing 12-month period, and in 2014 and 2013 had almost no free cash flow. Yet, it has paid dividends in these periods.

Exxon has paid smaller dividends, but it reported $5.5 billion in free cash flow for the past 12 months, $12.1 billion in 2014 and $11.2 billion in 2013. Clearly, Exxon wins this round.

The bottom line: Chevron is a better growth generator and Exxon is the sturdy and stable dividend income-giver. Simply put, if its dividends that make your day, we suggest you go the Exxon way.

For additional dividend champs that the market often ignores, read our free report.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.