I have a Lull P5: mine is passive, Fralin PJ pups, maple top over ash body, RW board, 35" scale, 4+1 headstock. It definitely has the old school look. The passive tone isn't modern, but I wouldn't call it old-school. I suspect this is because of the 35" scale, but then again it could be due to the high-mass bridge, or other factors (probably a combination).
I like the Lull a lot: fit and finish are excellent. Probably because of the ash body it has very snappy tone: sounds great for slap even without the J pickup engaged (I never use the J pup). It also growls nicely (again, even without the J). The alder-body models probably offer more of the traditional P-bass "thump".
Playability is definitely new-school, however. The neck is slim and fast. I love the sexy satin finish, but the profile is a very shallow C, which I find unsettling because to me, a P-bass should have a chunky neck.

That's not such a big deal, but string spacing at the bridge is a genuine distraction to me: it's a fairly narrow 17mm, as opposed to the Fender-standard 19mm (3/4"). I can hang, but can't get completely comfy. YMMV.
I've auditioned the Fender Precision 5 a few times: the older model with 5-inline headstock and 9V preamp. Playability was perfect for me. Whereas the Lull P5 has a genuine P-bass body shape, the Fender P5 is scooped deeper on the lower cutaway for access to additional frets. The asymmetrical split-pup on the Fender bothers me for some reason. I also didn't care for the big bridge bucker, and wasn't thrilled with the preamp. The newer Fender P5 basses have 4+1 headstocks (which I prefer), and an 18V preamp which supposedly sounds much nicer.
There are a bazillion 5-string Jazz clones, but we P-bass lovers don't have many options. The Lull serves me well enough: isn't perfect (for me), but I prefer it to the Fender. I've emailed both Dan Lakin and Roger Sadowsky asking for a vintage-style Precision 5 string, but unfortunately neither has plans to build one (the PJ Sad is a killer bass, but it looks like a J).
P.S. The Benevente '51 model does have tons of mojo, but I prefer split-pup P-basses.