* Power/Toughness and other effects
No, he will be 3 either way.

Daxos's ability is a Characteristic-Defining Ability, as defined in 604.3a: It defines the power/toughness, it is printed on the card, it doesn't directly affect the characteristics of other objects, it is not granted to itself, and it is not only set conditionally.

As described in 613.3, Layer 7a is where Characteristic-Defining Abilities are set.  Effects that set power/toughness to a specific number that are not Characteristic-Defining are set in Layer 7b.  As such, Daxos's ability will always apply first, then Harmonious Archon will always overwrite it.

It is also worth mentioning that while Layer 7 has multiple sublayers, 613.2 specifies that in Layers 1-6 that Characteristic-Defining abilities are always applied before any other effects.