Probably, that Fe3O4 contents more iron than Fe2O3.

i will suggest you possibly search around for adequate information from published reports on Indirect interspecies electron transfer (IIET) process among methanogens particularly when iron is employed in the anaerobic system. several reports have been published on the use of iron to enhance methane generation process. i further suggest to you to donwload this article for further leads on you subject matter.. Abdelsalam, E., Samer, M., Attia, Y., Abdel-Hadi, M., Hassan, H., Badr, Y. 2017. Influence of zero valent iron nanoparticles and magnetic iron oxide nanoparticles on biogas and methane production from anaerobic digestion of manure. Energy, 120, 842-853

What happens, as the nanomagnetite Fe3O4 and γ-Fe2O3 have excellent magnetic properties, which allow them to be used as soft ferrites and for biomedical purposes due to their biocompatibility and biodegradability. In an anaerobic digester it is important to maintain the O2 condition null (coming from the external medium), and even within the reactor to favor this consumption, since the biogas is produced by methanogenic archaea that are strict anaerobes.

Therefore, when the reaction conditions favor the oxidation of FeO (absence of a reducing atmosphere), the product will be Fe2O3.

4Fe3O4 + O2 → 6Fe2O3

On the other hand

Iron oxide (Fe2O3) reacts with sulfides (H2S) to produce iron sulfide (Fe2S3) and water (H2O):

2 Fe2O3(s) + 6H2S(g) →2 Fe2S3(s) + 6 H2O(l)

Fe3O4 has both Fe+2 and Fe+3 in its structure. They might have better role in interspecies electron transfer because this is what it is mostly used for in AD. As Philip Antwi has mentioned, you should focus on this process for more understanding.

in fact, the more accurate probability of adding more one than the other is STABILITY, as the first is less stable is more "easy", to use an analogous term, for microorganisms obtain the Fe ion of a less stable compound another with greater stability. It must always be remembered that the reactions in AD occur simultaneously. Anyway, this is more complicated than it seems.

1) It is known that in Fe3O4 oxide iron atoms are contained in combined (II and III) oxidation state. The electron can hop between Fe2+ and Fe3+ ions in the octahedral sites at room temperature imparting half metallic property to magnetite. The magnetic moment of the unit cell comes only from Fe2+ ions with a magnetic moment of 4μB. Deepa Thapa, V.R.Palkar, et.al “Properties of magnetite nanoparticles synthesized through a novel chemical route” Materials Letters. Volume 58, Issue 21, August 2004, Pages 2692-2694

2)Fe2O3 can be attacted to a strong, external magnetic field. Fe3O4 can be attacted even to a weak external, magnetic field

3) electric conductivity of the Fe3O4 better than Fe2O3

what is the role of Fe2O3 in anaerobic process??????

Pease write the answer with refrence,

I think the most different is the ability of electron accept. Electron is released in fermentation. When Fe(III) is present, it will compete with H+ to accept electron, and thus related Iron reduction bactria can obtain more energy from such electron transfer and thus presents higher activity. However, the eletron accept ability for Fe3O4 is weak due to its valence state, and so its role changes. However, Fe3O4 presents high electron conductivity, so that it build a bridge (DIET) for fermentation bactria and hydrogenotrophic methanogens instead of H2