Specifically, I read the options as:
Cold-sim VR in the matrix (p.229): Data Processing + Intuition + 3D6
Hot-sim VR in the matrix (p.230): Data Processing + Intuition + 4D6, +2 dice on all Matrix actions
Cold-sim VR when rigging (p.266): Physical initiative + 2D6
Hot-sim VR when rigging (p.266): Physical initiative + 3D6, +1 die on all Matrix tests
Physical initiative includes at least the standard 1D6, so the number of initiative dice ends up being the same, but you use Reaction instead of Data Processing for rigging initiative. This also implies to me that you can boost your rigging initiative with things like Cram or the Increase Reflexes spell (which don't say they're incompatible with other initiative enhancements). I don't believe that's possible for matrix VR initiative, since it replaces your normal initiative rather than modifying it.
Am I reading that all correctly? It makes sense from a game design perspective that riggers would use Reaction as part of their initiative, but there's no attention drawn to the fact that VR initiative is calculated differently for rigging vs. matrix, so it makes me wonder if I'm missing something.
More generally, I'd really appreciate some clarification -- ideally in the errata -- about which initiative boosters are compatible or incompatible (e.g. per RAW I believe Cram works with Wired Reflexes but not Synaptic Booster) and whether they transfer between physical, VR, and astral initiative.