Removal of existing asphalt roof

Both methods can work, as can just installing over the deck without any insulation (but with underlayment). A lot depends on the product being installed and its requirements. A lot also depends on the home's construction and ventilation as well as on what the homeowner wants to accomplish with their new roof. Going over purlins can make the roof harder to walk and potentially more prone to uplift issues. Going over insulation can also make it harder to walk compared to direct to deck. However, the thermal breaks created by these assemblies can be helpful especially with homes prone to condensation or ice dams. Thermal breaks also enhance energy efficiency. Talk to your contractor or your manufacturer about your goals and let them help talk through the options and the positives and negatives to each.