I've never played a Pedulla, but I love my Genesis. It is very much a super jazz/jazz on steroids/etc. bass, beefy with lots of jazz bass bark and growl. The one you pictured has Bartolini 59Js, which are split coils so they stay nice and quiet even if you solo the neck or bridge. There are some out there with soapbars, but i've never played one of those.
The Genesis is a full size bass! 19mm spacing and the body isn't downsized at all. It's very well designed, nice contours, so very comfortable. The size is fine with me; I'm 6' 0", kinda long arms. I've seen some players mention that it felt really big on them, though, so if your preference is for smaller body basses you might find it kinda big. The neck to me doesn't feel thin/"fast", but it doesn't feel particularly big either, feels substantial but comfortable. It's a full 3" at the heel, a bit bigger than a Fender 5. Big enough that with 19mm spacing the strings aren't right on the edge of the fretboard, which I like.
Modulus had a new version of the Genesis at the last NAMM show - hybrid CF/wood neck, but a traditional jazz bass body (pickguard, chrome control plate, etc.), haven't seen anything more since then though.