Random peer selection is used by numerous P2P applications; examples include application-level multicast, unstructured file sharing, and network location mapping. In most of these applications, support for a heterogeneous capacity distribution among nodes is desirable: in other words, nodes with higher capacity should be selected proportionally more often. Random peer selection can be performed over both structured and unstructured graphs. This paper compares these two basic approaches using a candidate example from each approach. For unstructured heterogeneous random peer selection, we use Swaplinks, from our previous work. For the structured approach, we use the Bamboo DHT adapted to heterogeneous selection using our extensions to the item-balancing technique by Karger and Ruhl. Testing the two approaches over graphs of 1000 nodes and a range of network churn levels and heterogeneity distributions, we show that Swaplinks is the superior random selection approach: (i) Swaplinks enab...