Yeah, it's the same engine.
http://www.jagweb.com/aj6eng/v8_performance.html
The LS 3.9L is a slightly cheapened Jag 4.0L that has had the bore reduced .05mm for marketing (so Jag buyers get a bigger engine). Also, the Jags have variable valve timing, which the LS didn't get until '03.
On the lack of bottom end, I hear you when you say it's ironic for such a comment to come from a 3.9L owner. However, the LS's 5-speed tranny does a great job at compensating for that. What's 1st gear on a 4R70W? 2.4? 2.4 x 3.27 rear = 7.85 torque multiplication in 1st gear. For an LS, it's 3.25 x 3.31 = 10.76.
The 3.9L in the LS feels a lot bigger than it is. I'd like to see a dyno chart of it. It'd be interesting to compare area under the curve to a Mustang 4.6L.