This is true for me as well.
Gotta love TB. Discussions about Thunderbirds devolve into talks about neck dive. You can't talk about StingRays without having a "weak G string" debate.
Here's the deal. Within two seconds of picking up a Gibson Les Paul, I can tell that the neck is "special.". Somehow, for all its faults, the Gibson managed to get a gret neck profile on my Thderbird as well.
Can we debate T'bird tone instead? I seem to have more low end with my Gibson than anything short of my active basses (with the low end boosted.). I am finding that these basses love an Ampeg 810e, and can get a little weird in the midrange with anything else. The low end overpowers everything else to the point that you feel like there is nothing but low end. I cut some lows at the amp and this really helps the mids and highs come through. Even so, I run moretop end at the amp than I do with other basses. When I get it dialed in though, the tone is smooth and even in a way that I never can get single coils to be. I was concerned that the smooth tone would get lost in the mix, but this doesn't seem to be the case.
On a side note, I am taking Tbird1958's advice and working on my pick technique. My skills with a pick are very limited, but both the tone and he Gibson setup are built forplaying with a pick. (Fingerstyle still sounds good, though.)