First check out the thread that goes over the delay tone in depth.
Second I have owned the Vox modeling stuff and did not have any luck finding any great sounding tones.
There are a few usable tones but I had a hard time finding them.
Third and most importantly, Its not just delay that makes Joes tone. Correct me if I am wrong guys... Its his use of a dry and delayed amp. The Marshall is the delayed one as it has a great clear sound excellent for delay. He runs it thru the effects loop not in front of his amp. This is very important.
The thick tone behind it is a product of his unbelievable collection of high priced amazing sounding amps, and his awsome collection of Les Pauls and other assorted dream guitars. Let not even include the fact he is an amazing player with a knack for dynamics.
This is only a start.
I have found I can get a pretty good thick sound from combining my Twin with a Vox AC 30. I use Fulltone Effects for a very thick creamy yet clear sound. The vox helps with the clarity. I run the delay thru the Vox's effects loop.
I use a 58 reissue Les Paul.
This will get you close but I am still not in the same ball park of joes tone. I am just trying to create something similar with my budget.
Good luck.
Jeremy Galvan