Both are autocephalous/self-governing churches.
In terms specifically of going to a service at these two, of the two of them the OCA is
more likely to have a mostly English liturgy. In my experience the Greek Churches retain their liturgical Greek and may then have things repeated (Holy Gospel, homily) in English. However we have an OCA parish near my home which services are in Slavonic.
This Thursday is the Feast of the Ascension so I’d expect both of them to have the festal Vigil Wed. night (not a Eucharistic liturgy) which would be glorious services and can run a couple of hours, the Greek festal vigil being shorter than the OCA, in my experience here in CA, and celebrate the Divine Liturgy on Thursday, the Feastday.
If either of the parishes is named “Ascension”, as is our local Greek Orthodox Cathedral, then Thursday would also be their altar feast, a hugely important day for a parish, and if he can the bishop would come for an hierarchical Divine Liturgy.

The music in a Greek Orthodox Church would almost certainly be Byzantine chant. In the OCA it would more likely tend toward Slavic chant.