No, and frankly there's a lot of misconceptions out there being repeated.
A P has stronger
mids than a passive J, and we
hear those low mids as these huge deep lows, but the fact of the matter is the actual frequencies we're hearing are not the low lows. A J can actually put out stronger, lower fundamental lows than a P due to the placement of the neck pup.
For another thing, if your J seems bright then use the tone knob! That's what it's for. Also read up on reggae technique, because proper technique is what generates that deep throbbing boom
on any kind of bass with any kind of strings. I have rounds on my J and can get a super wide deep boom just by playing with reggae technique.
A P is a good "shortcut"- roll back the tone, throw on some flats, and you don't need technique to get a big fat boom.