(I am talking about もの as a standalone noun outside of compounds. The kind of もの used after the 連用形 form of verbs (忘れ物 etc.) is usually 平板型 (though there are many exceptions))
I feel like 尾高型 is in a way the "default" pitch of もの but I do come across the 平板型 pronounciation as well. I haven't been able to make any inferences as to which pronunciation is used in which environment.
I tried to consult the (electronic) NHK accent dictionary and it just gave me two rather cryptic examples: 物(〜がよい) where it is 平板型; 物(〜をもらう) where it is 尾高型. So I guess the succeeding particle is what makes the difference? What about the other particles?