To start answering your question, I'm going to deviate from the question itself and explain the benefits of each hand position.
1) Supinated (standard grip) curls lift primarily with bicep brachii, stabilised by the forearm flexors.
2) Neutral (hammer grip) curls lift with bicep brachii and brachialis (a deeper elbow flexor), with some assistance from brachioradialis, stabilised by the forearm flexors.
3) Pronated (opposite to standard grip) curls lift with bicep brachii and brachioradialis, with some assistance from brachialis, stabilised by both forearm flexors and forearm extensors.
Bicep brachii has 2 main movements: forearm flexion and supination. If only one of these movements is present in an activity, then the muscle cannot work through its full ROM. If you are seeking to increase the ROM in which bicep brachii works, then start a curl with your elbow out straight in full extension and your hand pronated. Gradually rotate into supination as you move the elbow into full flexion.
Now, the muscle which goes through more ROM than any other muscle involved in an exercise does not automatically do the most work. Likewise, going through a greater ROM does not automatically improve the results of the work performed. Sometimes you make gains from doing a very heavy weight with only a 10degree ROM, other times you make gains from doing a lighter weight with a 150degree ROM. So I'd look into things such as torque and gravity, as well as personal experience before deciding that one method is best. The very fact that many different methods may all produce the same apparent result, and that it's widely recommended that we change some exercises frequently, indicates that it may be best for one individual to keep doing the same exercise for 6 months, while another individual may benefit most from modifying the exercise every 6 sessions.
