While Mexico's economy is strongly tied to the U.S., Australia is highly dependent on the commodity trade with its Asian neighbors.
"In contrast, if we look at trading partners, Australia is heavily exposed to China and we're continuing to see mixed data at best out of that region," Pepper said.
Even though Chinese growth is much faster than expansion in developed economies, the first-quarter data came in lower than expected at 7.7 percent, down from 7.9 percent in the previous quarter. And Chinese equities have taken a breather—the MSCI China Index has lost 2.23 percent over the past three months.
Weakening China growth and recent Australian rate cuts have taken the air out of the Aussie dollar. The currency lost around 7 percent against the U.S. dollar in just over a month. And some analysts expect the Australian dollar to fall even further.
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On the other hand, there is brighter news coming out of Mexico as the new president is moving boldly with his reform agenda, which has improved sentiment.
"It looks like there is a good chance that the [reforms in Mexico] will be implemented by the current government. That government has good political momentum," Pepper said.
Barclays forecasts that potential growth in Mexico could increase from 4 percent to 6 percent as reforms take hold, leading to additional peso appreciation. But reaching that potential may be some time off. The Mexican government on Friday lowered its growth estimate for 2013 to 3.1 percent from 3.5 percent after sluggish first-quarter growth.
The Mexican peso has strengthened more than 8 percent against the U.S. dollar so far this year, wrote Alfredo Coutino, a director at Moody's Analytics, in a note. But he does not see Mexican authorities taking action at the moment as "they consider that the peso is still undervalued with respect to the pre-crisis level of 2008."
(Read More: What's Wrong With This Forex Picture?)
The peso, however, could reach levels that hurt the country's competitiveness by making exports too expensive, he continued.
"Before that point, policymakers will remain passive and the peso will continue to strengthen," Coutino wrote.
Pepper said that there is another currency pair that can serve investors well—the Aussie against the Canadian dollar. Like Mexico, Canada is exposed to the U.S. economy—75 percent of Canadian exports go south of the border.
He expects the loonie to be "the currency that is likely to outperform in the commodity sector."
_By CNBC's Anna Andrianova. Follow her on Twitter