By depth do you front-to-back (fretboard-to-back of the neck), or are you talking about width of the fretboard?
Either way, I think the necks on these are pretty comfortable. I have an EB-0, and while it's the short scale version, I seem to recall it being comparable in width/depth to the EB-3. Just, you know, shorter. It's not jazz neck narrow, but it's at least as comfortable as my jazz. Neck dive is a thing for sure, especially on the full scale EB-3. If you're sitting don't worry. A wide, suede leather type strap helps, too.
You'll definitely get a different sound, just about opposite of what a jazz bass is. These basses are deep and muddy (hence the term "mudbucker" for the pickup), and that's the draw, of course. With the EB-3 you get the benefit of the bridge pup to even things out just a bit.
Another thing to note is that the stock neck pickup is very low impedance and very low output compared to a lot of other bass pups. There are several aftermarket options for a hotter signal, but I just turn up the volume on one of my preamp pedals when I play my EB-0.
Eat all your veggies. And don't bang the dillies.