In English, nominalized verbs have only one form regardless of the thematic relation of its possessor:
In (1), the robot is the agent whereas in (2), it is the patient.
Are there any languages in which the nominalized verb has different forms depending on the thematic relation of its possessor? That would seem like a very useful distinction to be able to make.
EDIT: Re-reading your question, I've just realised you were looking for a difference on the nominalised word itself, not in the syntax of the links to the subject and object of the action, but I'll leave my answer as it's potentially interesting.
Māori marks a distinction on nominalisations of transitive verbs. I'll show the non-nominalised active and passive sentences first.
Accusative objects are marked by the preposition i. Agents of passive verbs are marked by the preposition e ("by"). Passive verbs are formed from active verbs through the addition of a suffix of the form -(C)(i)a (although there are a few that do not quite fit this pattern, such as -ina). Dictionaries list one or more passive suffixes after transitive verbs.
(1) Active:
kua patu ngā tamariki i te kurī
PRF beat DEF.PL children ACC DEF.SG dog
"The children have beaten the dog."
(2) Passive:
kua patu-a te kurī e ngā tamariki
PRF beat-PASS DEF.SG dog AG DEF.PL children
"The dog has been beaten by the children."
Both patu and patua become nominalised as patunga. Which one's meaning is supplied to the nominalisation is indicated by the type of possession, as well as the particle used to indicate the other argument, if present.
Māori and other Polynesian languages make a distinction in possessives between what can broadly be regarded as inalienable or subordinate possession, marked with a and alienable or dominant possession, marked with o.
(Which one is used in which case can be highly idiomatic, which is probably the reason why they're usually simply referred to as a-possession and o-possession. For instance, all food and drink is possessed with a, except wai (water), which is possessed with o (but NOT words for other beverages that happen to have wai as their head, such as waireka "fruit juice"). Pets and other animals take a-possessors unless the animal is used for conveyance, so tāku kau "my cow", but tōku hōiho "my horse". I will gloss them as AL and INAL here just as a reminder, since you can see the thematic vowel anyway.)
In nominalisations of transitive verbs, what would be an active subject (agent) in a sentence, is indicated by a-possession. What would be a passive subject (patient) is indicated by o-possession.
(3) Nominalisation of active sentence:
te patu-nga a ngā tamariki i te kurī
DEF.SG beat-NMLZ AL DEF.PL children ACC DEF.SG dog
"the children's beating (of) the dog"
(4) Nominalisation of passive sentence:
te patu-nga o te kurī e ngā tamariki
DEF.SG beat-NMLZ INAL DEF.SG dog AG DEF.PL children
"the dog's beating/being beaten by the children"
In nominalisations from other verb types (intransitive verbs, experience (or middle) and statives (or neuter verbs)), the role of the subject is indicated by o-possession. It's only the subject of an active, transitive verb that is indicated by a-possession in a nominalisation.
(5) Nominalisation of an intransitive verb:
te tae-nga o ngā tamariki
DEF.SG arrive-NMLZ INAL DEF.PL children
"the children's arrival"
The examples (3) and (4) are from Harlow, R. (1996). Māori. Lincom Europa (ISBN: 3-89586-120-0). All other examples are my own.
