I was shocked rubber ducks weren't mentioned. A clear distinguisher.
HK is one example of the Conrad having a better location than the GH, but Tokyo is the opposite with the Grand Hyatt being in a much better location than the Conrad (Roppongi Hills vs Shidome). Both locations price accordingly with the HK GH usually at a discount while the Tokyo GH at a premium.
Grand Hyatts may be positioned lower in your view but are also more accessible in key business cities. Seoul and Taipei come to mind in Asia, and New York City only very recently had a Conrad added in.
Overall Hyatt and SPG brands match well, but not as neatly with Hilton. grand hyatts and Westins is probably a good comparison. While Andaz is probably a hybrid between a LeMeridien and a W. Vs Hilton i find most Conrad's to be positioned in between a Grand and a Park Hyatt.