Why do Airbus and Boeing have different approaches to bleed air systems? Reading Wikipedia and other questions like this, made me curious as to why Boeing uses bleedless architecture for its B787, while Airbus thinks differently for its A350 XWB (and Rolls-Royce thinks the same).

Both companies switched to composite materials for their new aircraft so they agree about some new technologies, but not all, since they have different approaches to the air systems.

Why did Airbus remain more conservative on this topic (even if its model is about 5-7 years younger than the B787)? What is Airbus's argument to sustain this choice and how does it compensate the disadvantages (cited by Boeing in linked post) of the traditional bleed air systems?

To be more precise, development of new technologies bring both companies to share many new common approaches because advantages are clearly evident, for example: glass cockpit, composite materials, wing extremities (sharklets/raked wingtip/winglets), bigger fans, but they are different ideas about others, such as control yoke, flight envelope, chevron onto engines and, effectively, bleed air.

I found information about "why" Airbus choices to avoid chevrons or prefer a side-stick joystick for example, but not about bleed air systems
Nobody can tell you for sure without insider knowledge, and insider knowledge would be confidential in this case, but ultimately it boils down to risk management. Every new development carries a risk of budget and deadline overruns and of problems surfacing in operation and the manufacturer needs to be reasonably certain they can put the product to market before they run out of money.

When Boeing started developing 787, the 777 was selling well, so they had the budget reserve to risk more innovation. And it did have some problems in operation with battery fires. Airbus was in worse position when developing A350, so they stuck to more tried technologies to keep the risk lower.