As you have discovered, there are two popular places where the tissue can be harvested. The first is from the patellar tendon just below the kneecap. This graft is referred to as the bone-patellar tendon bone (BPTB) graft. As the name suggests, the harvested tendon comes with a tiny piece of bone.
The second is a hamstring graft. Tissue is taken from two separate sites of the hamstring muscle. Each graft is folded over to form a quadruple (four-part) graft. This is the strongest graft and referred to as quadruple hamstring graft.
Either source of tissue (patellar tendon or hamstring) can be an autograft (your own tissue) or an allograft (tissue from a donor bank). There are indeed advantages and disadvantages for each one.
Orthopedic surgeons from the Department of Orthopaedic Surgery and Sports Medicine at the University of Kentucky have published an article stating their preferences. This is probably a good list to start with:
There are risks and benefits with any soft tissue graft. As each patient faces the decision of choosing one over the other, conversation with the surgeon is important. Selecting the graft type is a personal choice based on each patient’s needs, activity level, goals, and preferences. The decision will be influenced by surgeon experience and preference as well.