So, in essence, what Bucketboy said: all else being equal, a shroud will SUBSTANTIALLY outperform a moderator of equal internal architecture, post-muzzle-length, and diameter. I say this, not as a guess, but because I've actually performed a substantial number of experiments and documented a handful of them in this thread:
https://www.airgunnation.com/topic/fx-crown-bespoke-moderator-tesla-gas-diode So if you're curious, it is a great read and the answer to your question is actually buried in there. I would, however like to pour a little data directly on this fire for those not interested in wading through 7 pages of long posts. I'm going to simplify things a little and skim over some details for the sake of brevity, but this should give you a reasonable idea:
Here is a moderator on an unshrouded .22 caliber airgun:
And here is the same mod on a shrouded .22 caliber airgun:
As you can see, there is a SUBSTANTIAL improvement in sound attenuation, notable not just in the lower peak but in the post peak sound. (again there were a few simplifications in here)
The reason for this is reflex volume, That air, after it is initially deflected/delayed, wants to go in all directions, so this gives it a direction to go in other than forward out the muzzle. That allows the moderator to experience lower pressures, and thus makes it quieter. I should add that, if you're in the stage where you're designing and building mods, not just buying them, this allows you to focus more of that precious space toward sound damping and less on flow delaying. This is why, when asked, I recommend dramatically different moderator configurations for mods on shrouds vs. direct muzzle thread. No two ways about it, it is a lot harder to muzzle that bark if you only have the moderator's volume to contain it.
Speaking of damping sound, it is also worth noting that sound loves to reflect and run up and down hollow tubes. Putting some sort of damper in your shroud can also measurably improve your sound attenuation. I actually posted an entire thread to this effect, which if you're curious might also be worth a quick skim:
https://www.airgunnation.com/topic/shroud-damper/ As far as the question of shroud or mod goes though, I'd argue it is a false dichotomy. As mentioned above, for scope clearance reasons and for internal architecture reasons, relatively modest diameter shrouds are best. But when you get to the mod itself, the best overall performance generally comes from designs of slightly larger diameter than you'd want your shroud. (again, ref. my big test of all the major designs on the market
HERE.) So the optimal solution, in my opinion, would be a shroud at the back, with a damper, and then a moderator at the front. The FX shroud design is quite a good one, in my opinion, where it is retained NOT by the gun's muzzle, so differential heating shouldn't affect POI. It also is silly easy to service.
Just my 2c. I hope it was helpful/informative.