Does Overwhelming Splendor remove a creature's printed activated abilities or only those granted by other effects?

Overwhelming Splendor's effect states that creatures your opponents control lose all activated abilities. Under CR 112.6, 'lose all activated abilities' removes every activated ability the permanent currently has, regardless of whether it was printed on the card or granted by another effect (an Aura, Equipment, static ability, etc.).

An activated ability is defined in CR 602.1 as any ability written in the form '[Cost]: [Effect].' This includes mana abilities, tap abilities, sacrifice abilities, and any other cost-colon-effect structure. All of these are stripped by Overwhelming Splendor's continuous effect.

This is a continuous effect that applies in layer 6 (ability-removing effects) per CR 613.3. Because it operates in that layer, any abilities granted to those creatures by effects in the same or earlier layers are also removed when the layers are evaluated in order. The only abilities that could survive are those added in a later timestamp within the same layer, though Overwhelming Splendor typically locks things down comprehensively.

Concrete example: Your opponent controls a Llanowar Elves (which has '{T}: Add {G}') and equips it with Sword of the Animist (which grants '{T}: ...'). Under Overwhelming Splendor, both the printed mana ability and the Equipment-granted ability are removed. The Elves cannot tap for mana or use any other activated ability.

Note that triggered abilities and static abilities are NOT removed — only activated abilities. So if a creature has a triggered 'whenever' ability, that still functions normally.