I believe he picks up the Fender again for Get Over It. I always liked his Fender tone for that concert. It's very growly, but still has a lot of note definition. It's actually what I think a pretty prototypical good Jazz Bass tone should be. I guess that goes to show how subjective some of this stuff really is, and how everyone "hears" different things when they listen to music.
Anyways, as a Carvin owner (LB75, hopefully Icon 5 by the end of the week) and a Jazz Bass owner (standard Mexi Fender J, Squier Jazz Deluxe V, SX Jazz 5-string with aftermarket Barts, plus I've had my hands on many-a-Jazz throughout my playing years), here are my views. The Carvin is a modern instrument, through and through. It's very articulate and there's no mistaking that it has active electronics. The bass itself doesn't have an instantly recognizable tone like a Jazz, Ric, Stingray, or Warwick. However, what it lacks in personality, it more than makes up in its ability to just sound awesome in a mix. I've had sound guys almost freak out over how much they like its sound when they're getting a level on me at the beginning of the night. The first gig I played with it, my guitar player just couldn't get over how it sounded through the FOH. The only thing I don't really dig about the Carvin is that I've never really cared for the rear pickup soloed (it has J99s). I usually blend both pickups right down the middle and the rear pickup adds just the right amount of presence to the more growly front pickup; I just don't dig it soloed. The Jazz Basses, in my general experience, are a little more organic. They have an instantly recognizable tone. They aren't quite as articulate as the Carvin. Plus, I've always preferred a full active EQ to a tone knob. In my experience, it's just real easy to go overboard with the tone knob by going from adding some presence/note definition to becoming full on clank and excessive finger/fret noise. That's just my personal experience. The Jazz Bass is a classic tone and I don't think that it will ever fully go away. The Squier, of course, is a totally different animal all together. It's an active bass with a modern flair. It's a bit more scooped than the Carvin and doesn't punch through a mix as readily, IMO (I'd like to upgrade the electronics). I do prefer its slap sound over the Carvin, probably because its more scooped.
Bottom-line: I think that it's almost comparing apples and oranges. Even though the LB series is obviously another spin on the Jazz vibe from a cosmetic standpoint, they aren't very Jazz-sounding to my ears. One bass is a modern, hifi piece. The other is an old school bolt-on for a taste that likes there to be instrinic colorization with the gear. They are both excellent instruments. I love my Carvin, but I plan on owning a high-end MIA Fender Jazz one day. I wish they made a five-string version of the Geddy Lee, which is by far the best playing Jazz I've ever played. Wow, I really hope that my Icon gets delivered here today!