(caveat emptor! This is all impressions from read-throughs, not play experience, so take all this with a huge grain of salt...)
Arkadia is pretty light-weight. It's more of a "how to skin D&D in a Greek style" rather than a full-fledged setting or campaign. Its gods map fairly neatly into the regular Greek pantheon, and its few major cities reflect our stereotypical ancient Greece in a fairly straightforward way. The player options build on standard D&D characters; equipment lists are adjusted to reflect bronze age; and there's some new magic and monsters intended to emulate mythic Greece. It doesn't provide much in the way of new mechanics or anything. It also doesn't offer big plot line or anything, so the DM is on their own to build an actual campaign.
Theros is a much beefier book and a more complete setting derived from the
Magic card game. It's definitely it's own thing: certainly
influenced by Greek myth, but it's not actual mythic Greece. The pantheon and cultures are only loosely based on our "real" myths. It's got fewer new options for PCs, iirc, but also offers some new mechanics for the sort of heroic play the setting focuses on (namely things like omens and Piety). It also present quite a few hooks, small maps, and so forth to aid the DM in running a campaign. Like Arkadia, though, there isn't really any single over-arching story presented.
FWIW, there is a third setting called
Odyssey of the Dragonlords. I haven't fully digested this one yet, but i'd say it's comparable to Theros in its "accuracy:" heavily inspired, but definitely its own thing. It's got it's own history and pantheon, and (spoiler!) dragons. The book does offer quite a few new player options, monsters, and so forth, as well as some new concepts like Fame and Epic Paths. Importantly, this one is an actual campaign to high-levels, played out in several Acts and modeled on the trope of "epic great labors."
None of these settings, iirc, mentions common mythic Greek tropes like "the loyal friend;" commanding crews or armies; or nautical rules; etc. The concepts of "fate" and "destiny" are addressed in Theros and Dragonlords, though not especially deeply or innovatively, imo.
TL;DR
- Arkadia is probably closest to an "accurate" Greek setting, if only because you can easily swap out its fluff with actual mythic Greece; and because it explicitly offers some ways to stylize your D&D in a Greek fashion. But it doesn't have much story attached to it; the GM will have to build a campaign from scratch.
- Theros has much more to it, but as a MTG setting, also less truly Greek. The setting itself is well fleshed out, and it's got a little more story to work with, but no single coherent campaign is offered. Perhaps nice for an on-the-fly sandbox?
- Dragonlords is complete, providing a full setting and campaign to go with it. But it's not "truly" mythic Greece by any stretch. If having a prebuilt adventure path is important to you, though, this might be the one to go with?