The side with better logistics seems to always win. The ostfront is a good example of logistics overcoming quality. What is the clearest example of the reverse happening?
No single factor determines the outcomes of all battles and wars, this is true even for the most important one, logistics.
Usually when a side fights on home territory, can field bigger armies that are better equipped and fed, then have they have better logistics. Yet we can still find plenty of examples of such sides losing, like Agincourt:
The English had very little food, had marched 260 miles (420 km) in two and a half weeks, were suffering from sickness such as dysentery, and faced much larger numbers of well equipped French men at arms.
The vast majority of invasions & foreign wars. Whenever you choose to fight on foreign soil, you invoke a fairly dramatic handicap in logistics. If we limit the examination to conflicts where technology and equipment are roughly par, then distance to conflict becomes a significant discriminator in logistics. Defenders can count on frequent, if not ubiquitous resupply.
Rome - Conquest is the definition of poor logistics. Concentrate on the Eastern wars, or the frequent internal civil wars.
War of 1812 the UK trounced us from across the ocean. All logistics devoted to the USA had to be diverted from an existential conflict against an entire continent. Although the UK had equipment superiority, they were forced to fight us with their "C" team because the A team and the B team were busy fighting off everyone else in Europe.
Battle of the Nile - Nelson fought in the Mediterranean, near the coast of France. Nelson had lost his scout squadron and relied on luck to find the French. Their equipment wasn't radically different, but Nelson destroyed the French fleet. (the deciding factor was neither equipment nor logistics but boneheaded tactical decisions).
Vietnam - (arguably we didn't "lose", but I think that is outside the scope of this question.). US and French equipment was clearly superior, but their logistics were vastly inferior to the locals who lived among their supplies.
Falklands - The UK had a long logistic tail; the Argentine's could resupply locally.
Every carrier deployment in history. Carriers are about logistics.
The dichotomy you're drawing also assumes that the soldiers, sailors, airmen & marines are all fungible. They're not. The quality of the warriors decides many battles.