Providencia versus Centro? (Santiago de Chile)

Hello, I'm trying to decide where to live in Santiago and I have been recommended either Centro (Bellas Artes or Barrio Lastarria) or Providencia....

My main goals for a neighborhood is to have a good feria nearby for cheap grocery buying and parks for jogging/exercise. Bonus points if there is a basketball court and/or crossfit gym in the area as well.

Based on that criteria, which neighborhood in Santiago would you recommend?