In a nutshell, 2 for a nickel :) Since the lower four strings of these two instruments are the same, we might as well learn a bit of both, and at the same time. Meaning that the following method (s) follow right along side by side with one another. Learn some chords? Let's find a bassline? Got a bass riff ... let's find some chords. Got a piano? Oh look out !
This method works well to start a band with these instruments. The basics get everyone on the same page. SWap parts when somebody can't make the show. Then there's the theory to explore and potential evolutions as art matures.
So maybe do both or one or the other, or start a band, or add this method into your band, whatever works really, maybe even start another 'cyberband', with cats beyond your horizons, and use this web book as a way to meet up somehow and share music.
A note of truth. Branching out to other instruments can help to stay bizzy in tight gig markets. In my own, mostly guitar experience here in Alaska, instant dates when I got a real bass :)