That's entirely up to you. Both do exactly the same — hair, face, hands, body, washing up.
The difference isn't what they can do, but what you prefer: how the lather and the glide feel, during and after. Some swear by one, some by the other. Your own preferences decide — ethical, skin-related, or something else entirely.
Beef tallow — not vegan. Viking. A hard bar. The fatty acids — palmitic and stearic — are the same ones the skin produces itself. The lather comes quickly and is full. And it's economical.
Olive — vegan. Built on a bastille recipe: over 70 % olive oil. A completely different feel, during and after. The lather is creamy rather than bubbly and feels extra smooth against the skin.
Both kinds have washed whole cultures for hundreds of years. The difference was geography — Scandinavia had no olive groves.
Both need to sit dry between uses.