It really doesn't matter. At 19th St., you (sometimes) walk across the platform - maybe 20 steps. At Balboa Park, you get off the train and wait for the proper train at the same side. (The sometimes depends on whether you are on a train that goes through SF, or a Fremont train. If you are on a Fremont train, then you change at 19th St. always)

That said, I always take whatever first train to get me to the side of the bay that I want to be on. Given BART's reliability issues over the past few years, this way if something goes wrong, I'm much closer to where I need to be. This worked out quite well last year when I took the first train to the East Bay, got off in West Oakland, and then there was a service disruption (someone started walking down the tracks toward downtown Oakland). I left the station and took UBER home. Had I waited in SF, I'd have been stuck there for quite some time.