I assume the answer is "based on which verb is appropriate", so I've been trying to learn the difference between them. Based on the links above, here's what I've got so far:
- They both generally refer to twisting. There are cases where it could be read either way, because the meanings overlap: 「体を捻る・水道の栓を捻る・足を捻った」
- When you put a lot of force into twisting, it's ねじる. So you use ねじる when you're opening a bottle by (forcibly) twisting the cap off: 「びんのふたをねじって開ける」
- If you're twisting something with your fingers or fingertips, you use ひねる: 「ひげをひねる・スイッチをひねる・鶏をひねる」
- Metaphoric uses appear to use ひねる: 「頭をひねる・ひねった質問」
Does this seem correct?