It's depending on many parameters including energy consumed by absorption or capital cost. In low scale and capacity adsorption is recommended because of some advantages, low energy requirement, no solvent needed for absorbtion and any others

But for the adsorbtion you must consider that which type of adsorbents are more selective in NH3 or H2S capture. Some times activated carbon is prefered, but some times zeolite type adsorbents are more effective.

However it is recommended to search in the web to find conventional capturing methods of aforementioned gases 

Dear  Mahmoud Abdallah,

 Hydrogen Adsorption at low temperature, the metal oxide like Fe2O3

Fe2O3 + H2S → 2 FeS + S + 3 H2O

The studies of Oxide have a reactivit order as follow

Al2O3 < Cr2O3 < ZnO < Cu2O < Cr3O4

α-Fe2O3, which has a high theoretical adsorption maximum

Zink  & Copper oxide are also used to adsorbed H2S

Pressure swing adsorption  is a technology used to separate some gas species from a mixture of gases under pressure according to the species' molecular characteristics and affinity for an adsorbent material. Specific adsorptive materials (e.g., zeolites, activated carbon, molecular sieves, etc.) are used as a trap, preferentially adsorbing the target gas species at high pressure. The process then swings to low pressure to desorb the adsorbed material.The process known as chemisorptions.Ammonia adsoption in activated alumina Activated carbon.

For Absorption of Ammonia

Water- The ammonia is highly soluble in water can be absorbed in packed tower with counter current.

Regards,

Prem Baboo

Dual absorption columns; slightly acidic first column (ammonia removal) followed by zinc acetate in strong base second column (H2S removal). The acid column should be buffered since the absorption of the ammonia will change the pH in unbuffered solutions. Use something like a sodium acetate/acetic acid buffer.

The first question to be answered is the source of H2S and ammonia because source abatement in most cases is much more effective than aircleaning.

For H2S iron salts (ferric chloride or ferrous sulfate can be used to precipitate it as FeS. This method is used to reduce H2S problems in sewer systems due to anaerobic processes. If the source of the gases is aqueous the addition of iron salts to this "wastewater" could stop H2S emissions to a large extent. As both salts mentioned above are acid the drop of the pH would reduce ammonia emissions as the equilibrium between the gaseous form (odor) and the dissociated dissolved NH4 + results in a decrease of NH3 emissions. In principle an air purification system with sulfuric acid could be applied to remove ammonia from the air (NH3 + H2SO4 results in (NH4)2SO4 quite effectively. This process is applied in practice to recover ammonia from wastewater at wastewater treatment plants after stripping NH3 by air or steam. ammonium sulfate can be used as fertilizer (go to internet research).

Perhaps of some interest to this query ― On scrubbing ammonia with nitric acid (and related enthalpy balance) at this forum: https://www.researchgate.net/post/What_is_the_heat_reaction_for_Ammonia_gas_scrubbing_in_60_nitric_acid_solution