If it is possible, then what is the difference in meaning or nuance?
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Here’s the technical explanation, according to ‘Intermediate Japanese: A Grammar and Workbook' by Tsujioka and Hamano (2012, Routledge).
Basically they describe how Japanese verbs can be classified into two categories:
In general, eventive verbs take the particle
～を to mark the object of the action:
Stative verbs, on the other hand, generally use
～が to mark the object:
A verb like 食べる in its base form is an eventive verb, as it describes the ‘event’ of eating. However, when you add the ～たい ending to make the formation 食べたい, the verb takes on a stative aspect. It is now describing the state of wanting to eat. So it has both eventive and stative properties. It also assumes the grammatical properties of a stative verb, which means that you can use
～が to mark the object. These dual grammatical roles mean that either
～が can be used without much difference in meaning.
In summary, there is very little difference in meaning between your two sample sentences, according to the explanation by those authors. One final note is that if other volitional suffixes (such as ～がる) are used, the stative meaning is reduced and ～を is preferred. So it all depends on the level of volition introduced by the suffix.
The basic meaning of the both sentence are the same.
In this situation, you can emphasize your will by using が instead of を. So it is more natural to say "寿司が食べたい" in the following situation.