Shares of Australia and New Zealand Banking Group (ASX: ANZ) and Woolworths Limited (ASX: WOW) look cheap and offer big dividend yields.

But which – if any – is right for your investment dollars today?

ANZ Banking Group – dividend yield: 7.4% (fully franked)

ANZ Banking Group is Australia’s fourth-largest bank by market capitalisation and the most exposed to emerging markets in Asia. Until recently, ANZ’s Asian operations were huge selling points for the ‘super regional’ bank. However, fears of a slowdown in China and volatility in share markets across the region has seen ANZ Banking Group’s share price fall 32% over the past year.

Further signs of a slowdown in local credit markets are also dampening investors’ enthusiasm for holding bank shares. Nonetheless, it is worth noting Australia’s major banks have continually rebuffed their doubters to post bigger gains over the long-term. And with a price-earnings ratio of just 9x and its big dividend yield, investors will watch ANZ closely in 2016.

Woolworths Limited – dividend yield: 4.2% (fully franked)

It’s not been easy to be a Woolworths shareholder over the past 24 months. In that time, the share price of Australia’s largest supermarket operator has fallen 43%. Succumbing to shareholder pressure, Woolworths recently decided to scrap its Home Improvement business, which included the Home Timber & Hardware and Masters brands.

Speculation of a divestment of Big W and, more recently, its liquor business, has also been swirling, following Woolworths’ recent poor performance.

Woolworths recently revealed a half-year loss of $973 million and slashed its dividend in response to market conditions and pressure from the investment community.

Still, at less than $22 – compared to a price of almost $38 a couple years ago – Woolworths is expected to offer a robust dividend in the year ahead.

Better buy

Personally, I wouldn’t buy shares of either of these companies at today’s prices. ANZ is facing pretty stiff competition in local markets, more regulatory pressure from APRA, and China’s recent volatility isn’t likely to be forgotten anytime soon.

Woolworths, on the other hand, is playing catch-up after years of complacency, while competition in supermarkets is heating up. Moreover, without a Home Improvement offering, I can’t see where excess growth can come from in order to justify higher prices.

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Motley Fool Contributor Owen Raszkiewicz does not have a financial interest in any company mentioned. Owen welcomes -- and encourages -- your feedback on Google+, LinkedIn or you can follow him on Twitter @ASXinvest.

The Motley Fool Australia has no position in any of the stocks mentioned. 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. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.