Where are you coming from? Anza-Borrego and Death Valley are quite distant from each other (a full-day drive).
Death Valley would be my favorite, due to its more dramatic geology. Lots of interesting things to see there without getting too far off the road. If you've never been there it would be a great place to play 'tourist' and get a feel for the area (Scotty's Castle, Ubehebe Craters, the Dunes near Stovepipe Wells, Badwater, Dante's View, Artists Palet Drive, etc), then come back in a few years for hikes up Telescope Peak and other DV peaks. The campground near the visitor center is pretty decent, but it does get breezy in the springtime. If you've got a few $$$, stay at the Furnace Creek motel for a few nights. The DVNP website is pretty comprehensive and will contain all the info you'll need.
Also, if driving from 'Lost' Angeles to Death Valley, you have the option of stopping at the Antelope Valley Poppy Reserve (between I-5 and SR-14). Might be a pretty good spring flowring season with the good rains we've had this winter. Mid-to-late April is typically the best time for flower displays; check their website for daily photo updates.