A P bass is two single coils run in serial, which cuts the lows and highs, leaving plenty of lovely mids your amp can project and your ears are great at hearing. The average guitar humbucker is wired this way too, it's a great way of being heard. Think of the EQ being like the lips in a sad face :(
A J bass with both pickups on is two single coils run in parallel which works differently to serial, in that it cuts the mids, leaving lots of low lows and high highs. It's a great sound for some applications but, generally, you've got to get the mids back in there to be heard.
If you want to cut through with a J bass, only run one pickup and don't run a disco smile EQ on your amp.