No, they are pretty much both used in past tense. It just depends on your preference. Hope this helped. :)
2011년 7월 19일
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"I was worried about you." = past tense
"I worried about you." can be present tense, e.g. " Today I worried about you because you left your wallet at home.."
2011년 7월 19일
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I was worried...................here woried is an adjective.
I worried..........................here worried is past tense of to worry