I my opinion it is better to reserve the seats online in advance, for two reasons:
— If you wait to be in Europe, the train could be sold out.
— If you change your plans and want to take another train, you can obtain a refund of the original reservation (if it is possible), without going to a station ticket office.
Please note that reservations to Italy can be loaded in the Trenitalia app and exchanges are possible in this app, but, after an exchange, the reservation cannot be refunded by the original vendor.