Thanos can destroy the phoenix repeatedly, but it always returns — yet Thanos's cosmic power 'wins' each fight.
The mythological phoenix presents the same philosophical problem as fighting Deadpool — can you really win against something that comes back from the dead? But Thanos has cosmic-level tools that could potentially contain the phoenix permanently.
Thanos's energy projection can incinerate the phoenix, but it would rise from its ashes. However, Thanos has the intelligence and cosmic resources to potentially contain or redirect the rebirth — trapping the ashes in a stasis field, scattering them across dimensions, or using cosmic power to prevent the resurrection cycle.
The phoenix's offensive power — divine fire and healing tears — is impressive but unlikely to damage someone who tanks planet-busting attacks.
The phoenix literally cannot permanently die. Each rebirth potentially makes it stronger. Its divine fire burns at stellar temperatures.
Thanos dominates every exchange and has the intelligence to find ways to contain the rebirth cycle. His cosmic-tier durability shrugs off phoenix fire.
Thanos 'wins' every fight but may never permanently defeat the phoenix. His cosmic intelligence gives him the best chance of finding a permanent solution, which is why we give him the edge.
Phoenix also fights
Thanos also fights