I say its a bit of both. Ive changed bodies and left everything else the same and the instrument drastically changes. My friend had a stage brand. A plywood bass. Sounded decent at best (with upgraded pickups ceramic p dimarzios, a badass II and a newly shielded cavities and pbass harness with high end parts). I made a one piece brazilian oak body (one piece) and the instrument changed its timbre (I think Im using the right words) and sound... This wood sounds much more acoustic with mids and lows. almost like an upright this bass turned out to be. Also worth noting is when we changed all the stock parts when the bass still had the plywood what most improved on the bass was clarity and with the new pots, id say the amount of tone shaping the tone knob gives us.
SO TO ME... as far as experience tells me its not one thing. Its a mix. Can a crappy wood bass sound decent or even superb, probably given the right hardware t can be made to sound to someones liking or dream instrument... Every ear has its taste. Can superb woods with crappy electronics and hardware give wonderful tone and someone's dream tone, probably but i think it'd be much harder and probably have some setbacks such as hiss or what not.
ITS A COMBINATION OF BOTH. its not just the raw ingredients its how you cook them.