I am also a 1L and I'm interviewing with both the DA and the PD. I am not sure which is more prestigious in terms of the actual summer employment, but I'm pretty sure that the DA's office, if that's where you want to end up eventually, will view your PD experience in a favorable light. The employment materials that the DA gave me here said that they like to see experience with either the DA OR the PD's office; it seems like the most important thing is to get experience in criminal law, but it doesn't necessarily have to be on the "side" you want to practice on.
DA's office typically have tons of volunteer/clerk/externship opportunities during the year, so if you don't get a job with them this summer, try working for them during the year to make connections. The only thing is that you can't work for the DA and the PD at the same time, appearance of impropriety and all that. But it's fine to work for both sequentially.