A few comments:

1. The snap/crackle/pop is created by the engine via controlled misfire. The electronic ignition is delayed, resulting in loud misfired ignition. This article has an excellent overview of what Jaguar did to create the sound design in the F-Type.
   
2. Sound travels in longitudinal waves. For normal driving in the F-Type, that sound goes down the pipe into the resonator chambers. The perforations in the pipe (see cutaway photo below) allow some of the sound waves to diffuse into the resonator chamber, which enriches the tone of the exhaust note by adding deeper and broader notes (the "growl"). That growl comes at a price....since some of the sound energy is being diffused into the chambers, the cost of that tonal richness is lower sound volume coming out of the pipes.
   
   
   
3. When the Active Exhaust is turned on, exhaust is also diverted straight to the exhaust pipes via electronically controlled bypass valves (on the right in the picture above). This means less energy is going into the resonator/muffler unit and more going straight out of the car, which is why the car sounds louder but more "raw" with less growl when the active exhaust is on.

So what is the effect of deleting the resonator and/or installing an X or H pipe??

1. The popping will still happen because that is created in the engine.
   
2. The sound quality will obviously change. What X and H pipes do is allow the longitudinal sound waves traveling down both pipes to intermix and resonate....creating a little bit of a richer note. The downside is that it's nowhere near as rich as the resonator system because the waves aren't being bounced around as much. The upside is, less bouncing means more energy survives the trip to the tailpipe and the sound is louder.
   
3. If you delete the bypass valves you obviously also lose the switchable active exhaust function. But folks who install X/H pipes probably aren't looking for switchable sound anyway.
   
4. X and H pipes allow for a less baffled air flow and more balance pressure through the exhaust system, which can increase performance (the engine doesn't have to push as much air resistance / backpressure, heat is removed faster).

So the benefits are a louder, raw-er sounding car. The drawbacks are the loss of growl richness and probably the loss of active exhaust depending on how it's installed.

To me, one of the great qualities of the F-Type is the richness of its sounds(in tone breadth rather than loudness). That was one of the great innovations of the design. Even with the perforated pipes and the motorcycle pipes, the F-Type has a pretty "raw" sound which fits its aggressive posture.

So, personally I think the last thing the F-Type needs is a more brutal sound. Removing the innovative muffler design and replacing it with straight-through pipes is like taking a tourbillon watch, removing the tourbillon, and replacing it with a digital chip. Sure, it'll perform better, but you kind of lose the point of the whole thing.

That's just a personal opinion....there are totally valid reasons for doing the mod (performance gain, the hunt for loudness, etc) so this isn't intended to disparage owners who do the mod or vendors who sell pipes.

The main point of this long-a** post was to try to help answer the question

 

Someone post the Seinfeld Kramer "you just blew my mind" clip.

Absolutely superb education. So so fantastic. Thank you.

 

Ask and you shall receive

https://m.youtube.com/watch?v=Ih6XjO_fhrI

 

I did the X - pipe/resonator delete to my XKR. The result was a much louder exhaust and I thought a noticeable performance gain. The engine note however became more of a howl, think lamborghini instead of the traditional V8 rumble. I would get quite a grumble when my foot was off the pedal.

I did it more because in the XKR the exhaust wasnt loud enough. It really fixed that, though I preferred the throbbiness of the sound with the resonator on.

 

But the F-Types don't have resonators...they have an x pipe.