On the whole I’d say most basses I’ve owned have comfortable necks. Modern manufacturing is pretty good. I like narrow Jazz necks that are not too deep from the fretboard to the back of the neck. Too deep is just as uncomfortably as too wide IMHO. I’ve had P basses and Stingrays and can cope with the wider neck as long as it’s not too deep.
I’ve owned nearly thirty basses over the years (Fenders, Sadowsky, Xotic, EBBM, Warwick etc) and I’d say that the whole bass needs to feel comfortable on the strap, not just the neck.
The three Jazz style basses I now own are all very comfortable but sound different. Played unplugged the two with maple necks sound bright even though one has an alder body and the other a swamp ash body. The one with the rosewood neck sounds darker.
The unplugged sound makes a big difference when plugged in. But the thing that makes the most difference are the pickups IMHO. Two are passive basses with single coils (one under wound and one over wound) and one is passive but with active EMG single coils. I love the subtle throatiness off the under wound singles coils. The over wound are more mid sounding with less scoop. The EMGs are scooped (fewer winds) and very clean and punchy. Also very throaty and totally silent too. Fantastic for finger picking and slap because the preamp in the pickups just boost everything that bit more but without it sounding like an active bass. Definitely my go to bass but the others are great too.
The last thing is to EQ to taste to bring out the best tone in the bass. I used to boost bass and treble (smiley curve) but now I run everything flat but cut the mud a bit (maybe -6dB between 200Hz and 300Hz). Perhaps a small boost between 2KHz and 3KHz to add some sparkle. Makes a huge difference and really lets the bass breath IMHO.