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.
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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.