Jaguar engineered the exhaust to be very "subdued" so upgrading to a stainless exhaust may improve matters.
https://www.adamesh.co.uk/performance-parts-162-c.asp
Here's a video of someone who used those parts on their 2004 XK8 so should give you a good comparison :
The before & after comparison starts ~7:45 if you want to skip to the "good bits", in fairness it's quite a balanced video and he take it on a drive, going through tunnels etc with the new exhaust, cruising at 70mph etc.
My S Type 3.0 V6 is similarly subdued, i bought a pair of Adamesh rear silencers for mine (yet to fit them) which will hopefully give me a bit more of the V6 growl (a similar YT video suggests it will) but more importantly for me, will outlast any standard mild steel back boxes that would be a similar cost!
This was the video i saw for the 3.0 S Type if you're interested :
Also forgot to mention, the quality overall seems very good and i'm looking forward to getting them on there soon! Got a couple of other minor mods and a new set of tyres to go on (once i refurb the wheels) so hoping to get it all done in one go............