1. Reduction capacity of palladium hydroxide (Pd(OH)₂)
Chemical Properties:

Palladium hydroxide is not itself a strong reducing agent, but under the right conditions it can be converted to palladium metal (Pd) by thermal decomposition or other chemical reactions.
It can be used as a catalyst for hydrogenation reactions, facilitating the reaction of hydrogen atoms in hydrogen gas with other compounds.
Applications:

In organic synthesis, palladium hydroxide can be used to catalyse hydrogenation reactions, e.g. to convert unsaturated compounds into saturated compounds.
In the synthesis of some pharmaceutical intermediates or fine chemicals, it is used as a source of hydrogen to participate in chemical reactions.
Reduction reactions:

When palladium hydroxide is heated under appropriate conditions (e.g., high temperature, hydrogen atmosphere), it decomposes to palladium metal and releases water (evaporation):

[
\text{Pd(OH)}_2 \rightarrow \text{Pd} + \text{H}_2\text{O}
]

Limitations of reduction capacity:

Compared to other catalysts, palladium hydroxide has a more limited reducing ability, relying mostly on hydrogen or other reducing agents.
 

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2. Reduction capacity of palladium carbon (Pd/C)
Chemical Properties:

Palladium carbon is a highly efficient catalyst, where palladium is dispersed in the form of nanoparticles on the activated carbon, forming a very high specific surface area, which allows better access of the reactants to the palladium metal.
Given their nanostructure, palladium carbon catalysts have superior reducing power and are able to effectively catalyse hydrogenation reactions under mild conditions.
Applications:

Palladium carbon is widely used in a variety of organic synthesis reactions, especially hydrogenation reactions such as the hydrogenation of alkynes, olefins and aromatics.
It can also be used to reduce oxides to their corresponding hydrocarbons or oxygen-containing functional groups (e.g. carbonyls, ketones, etc.) to their corresponding alcohols.
Reduction mechanism:

In palladium carbon, palladium nanoparticles are able to adsorb hydrogen and provide hydrogen atoms through the metal surface, thus participating in the reduction reaction.
Advantages of reducing power:

Due to its large specific surface area and high catalytic activity, palladium carbon is capable of efficient reduction reactions at lower temperatures and pressures.
It can effectively and selectively reduce specific functional groups in complex organic synthesis while avoiding over-reduction.
3. Comparative summary
Palladium hydroxide: its reducing power is relatively limited and it is mainly involved in hydrogenation reactions under specific conditions or as a catalyst. It is suitable for some specific chemical reactions, but its overall reducing power is inferior to that of palladium carbon.

Palladium Carbon: It has a strong reducing ability and can effectively promote hydrogenation and reduction reactions under a wide range of conditions, particularly in organic synthesis, where it is widely used.

In practice, the choice of whether to use palladium hydroxide or palladium carbon should be assessed based on the needs of the specific reaction, the conditions and the nature of the target compound.