When playing with a band, you may feel differently. Many feel that playing a P by itself isn't that special, but in a band setting, it hits the sweet sonic space that bass is supposed to occupy. The only time my bandmates EVER made a comment about my tone was when I brought an American Standard P to practice. Unsolicited, they thought it sounded awesome - and they wouldn't know a P from a J from a Z, so it wasn't just appearance. This was after playing many other nice basses with the same group over a long period of time.
Also, there's a pretty substantial difference in the feel between a 4 and 5 string American Standard. The 5 is indeed a very big neck IMO.
I normally play 6 and 7 strings so I can play the neck just fine. It just seems kind of an excessive amount of wood for 5 strings. I've had a similar experience that you had with your band with my first Dingwall ABII. Our FOH engineer stopped what he was doing and came up to the stage. I thought something was wrong. He, and the band, then spent the rest of practice praising it's tone.