Vega's father, Otto Vega, is a general medical practitioner with offices in New York City and Miami. Her mother, Patricia Polanco Alvarez, also born in Santo Domingo, one of the first 3 Dominican Women to graduate as a Pilot. She was also a previous national titleholder who represented the Dominican Republic in 1980 at the Miss World pageant. Vega is the niece of the Grammy Award–winning singer Juan Luis Guerra.
After winning the Miss Dominican Republic Universe title, Vega represented the Dominican Republic in the Miss Universe 2003 pageant held in Panama City, Panama on June 3, 2003. She became the only titleholder from this country to win the title.
Vega was crowned in Panama. She wore a white evening gown during the competition, which featured strings of beads on the sleeves.
As Miss Universe 2003, Vega traveled extensively working with internationally recognized HIV/AIDS organizations including the Global Health Council, Cable Positive, amfAR, the Elizabeth Glaser Pediatric AIDS Foundation, and God's Love We Deliver. As a celebrity spokesperson, she was responsible for working with the international media to generate a better understanding and acceptance of AIDS/HIV epidemics and its prevention while helping to increase awareness, funding and resources for these key organizations.
As Miss Universe, Vega represented the Miss Universe Organization. Her "sister" 2003 titleholders were Tami Farrell (Miss Teen USA, of Oregon) and Susie Castillo (Miss USA, of Massachusetts).
Vega is the third among Miss Universe winners who also won the National Costume competition. Thailand's Porntip Nakhirunkanok won the award in 1988 and eventually won the crown then, Wendy Fitzwilliam of Trinidad & Tobago also won the Best National Costume and went on to win the 1998 Miss Universe crown.