In your opinion, what are the biggest advantages of system-driven entity component system (as described in your answer here) as opposed to putting logic right into components themselves (similar to how Unity does things)?
The advantages depend on the requirements of the game. The two styles are pretty similar really, so the biggest advantages are going to derive from personal style preferences.
The main differences I can see are when and where things get processed. With the system approach, you know that processing will take place grouped by component type. With the Unity approach, processing will take place by entity. For example, a simple set of entities (E1 and E2) with their components:
E1: C:Movement, C:Pathfinding, C:Attack
E2: C:Movement, C:Pathfinding, C:Attack
With Unity the overall processing order might look like:
E1:C:Pathfinding
E1:C:Movement
E1:C:Attack
---
E2:C:Pathfinding
E2:C:Movement
E2:C:Attack
Notice everything grouped by the entity. With a system like the one described in my answer everything would run grouped by system:
E1:C:Pathfinding
E2:C:Pathfinding
---
E1:C:Movement
E2:C:Movement
---
E1:C:Attack
E2:C:Attack
So in the end, the same code gets run, but the order is different. While Unity does have some features to change the order, like using Update() vs LateUpdate(), it's not going to group things by components for all entities.
As I said, the advantages of changing the order really depend on the requirements of the game. In a lot of cases, the design of a game could easily be adapted to work with either system. So when designing your own system, it's important to keep these differences in mind and make the design work appropriately for your style.