The reason why the PlayStation 3 version wasn't released outside Japan until 2019 was because of how difficult it was to release the Xbox 360 version in all major territories simultaneously. In Hideo Baba's own words:
"Tales of Vesperia was the first title in the series which was planned to be released simultaneously in Japan, North America and Europe. This was very difficult, and it was such a heavy burden for the team. So for the PS3 version, it was decided to reduce this burden and to develop it just for Japan."
Contributed by raidramon0
Exclusive to the Japanese PS3 version, costumes were available to be downloaded for the main characters, these costumes would be from other Namco franchises, such as a Klonoa costume for Carol, and Mitsurugi from Soul Calibur for Yuri
Tales of Vesperia sold so well in Japan that retailers there actually sold out of Xbox 360 consoles, 25,000 units were sold on the week of August 10th, in comparison to the 5,359 units sold the previous week.
Contributed by raidramon0
If the player uses Rita's Thunder Blade spell against Time Traveler/Dhaos when his health is below half during the Coliseum 200 man battle, Rita will instead perform Indignation and finish him off instantly. This references the intro of Dhaos' home game Tales of Phantasia, where said spell forced Dhaos into retreat. Rita will also be able to use Indignation freely from that point onward. This only applies to the PlayStation 3 version of the game.
Contributed by MightyKombat
Much like the previous games, Vesperia also features a coliseum-based Cameo battle set. This time around the player fights against major antagonists from the series, albeit with them using titles as opposed to their actual names. They are, in order:

Time Traveler: Dhaos from Tales of Phantasia
Sorrowful Queen of Darkness: Shizel from Tales of Eternia
Killer of Heroes: Barbatos Goetia from Tales of Destiny II (much like his home game, using any item during the fight will trigger his Mystic Arte)
Traitor to Heaven: Kratos Aurion from Tales of Symphonia
Contributed by MightyKombat