The original question seems sorta obvious; of course new is better...but more expensive.

 

I had the same type of noise on my, new to me, 06 LR3 V8 and the LR tech has found it to be the exhaust system itself. The baffles in the mufflers are going bad causing the noise. Same thing as you, only appears when under power, more apparent when in a high gear and going around 40mph, lagging the engine a bit, or going up a hill.
Fix is the fit a new exhaust from the cat back.

Hopefully this solves it for me, check your truck as well.
New OEM exhaust on order.

 

As it turns out, not only the exhaust was bad on this one. That was part of the problem. The real culprit, as it turns out, was the rear drift shaft. The splines and C/V joints are worn out causing the "rubbing" anywhere from 35mph-up. Fix is a new drive shaft.

So many noises, so many fixes! ARgh!