I am a BAEC Gold and Lifetime Platinum (Star Gold) on United Airlines, which allows me to compare experiences of OneWorld and Star Alliance in detail. Thus I can usually gain lounge access at most airports (unless I am using a non-aligned airline), which normally drives decisions in how to plan journeys either on a paid basis or using FF miles. But there are often other benefits too – for example the UA/Marriott partnership means that I get a gold Marriott card with the accompanying executive lounge access at Marriott hotels even on the cheapest senior tariff. On UA flights, I automatically gain access to the economy plus seating area (for those times I am not on a paid C class ticket) at no extra cost even on the cheapest economy ticket. I can also request an upgrade using miles, which would be provided at the gate on a space available basis in strict priority order, based on membership level etc. This avoids the frustration encountered on BA when flying on a PE ticket, having been unable to use Avios for an upgrade, only to find that there are empty seats in J class.
But it’s the route networks that count when you want to use FF miles. OW wins in Australia, whereas for Asia, Star probably wins because there are nearly always seats available on TG (even in business), provided you don’t mind BKK as a hub. On the other hand CX generally has good availability if HKG is a better hub. For South Africa it is Star. For South America it is OW, whereas for North America it could be OW or Star (especially for Canada), depending on where you want to fly. For me, Star wins in Europe since my local airport is BHX via a short inexpensive rail journey, allowing me to access LH, TK, SK etc if required.