The difference is that Wolfram wants an actual, single correct model in his hands, whereas Juergen is just talking about hypothetical computations that theoretically produce our universe as well as all the rest (with no hope of being discovered by us humans)

Effectively Wolfram is pruning the search space by looking for the simplest rules that he thinks have a shot of reproducing known physical features of the universe (eg special and general relativity, with a plan for how QM may come about), and then looking within that space for the specific flavor that is our universe. If you actually want to find the model via searching programs, this is the only realistic way to do it.

"But I suspect it's really more integrated: that everything is "just space", with the particles being something like special little lumps of connectivity in the network corresponding to space."

He's not saying it's definitely a network, he's just saying that he's going to start looking there because it intuitively makes sense. This seems reasonable for a few reasons. First, networks are the most advanced form of organization we currently know of. Second, it potentially provides a very simple explanation for many things, such as gravity. Third, the idea that matter is just really concentrated nothingness is just too cool not to look at. And it sort of makes sense if you believe in zero-point energy, which supposedly both general relativity and quantum mechanics predict (according to the free energy nuts).

/not a theoretical physicist

"Conclusion. By stepping back and adopting the Great Programmer's point of view, classic problems of philosophy go away."