Among these three titles, the one that is most worth your time to play is Phantasy Star Online 2. This is for one core reason: you are allowed to play it as much as you want. The major failing of both Samurai and Dragons and Gundam Battle Operation is that you can really only play the game for a short period of time each day without paying. The dungeons in Samurai and Dragons—i.e., the most enjoyable part of the game—will lock you out after 40 minutes of gameplay. In Gundam Battle Operation you are locked out after a mere three games (30 minutes).
When playing a free-to-play game, a lower standard of quality is expected and can be forgiven. However, most free-to-play titles still make a profit due to addictive gameplay combined with a store that charges a very small amount of real world money for in-game items. Phantasy Star Online 2 follows this "micro-transaction" model. Samurai and Dragons and Gundam Battle Operation, on the other hand, simply charge you to continue playing.
The simple fact of the matter is that people (myself included) are far more likely to return to a game they can play whenever they want for as long as they want rather than one that can only be played for a set amount of time. And because of this flaw, I personally doubt I will ever return to either Samurai and Dragons or Gundam Battle Operation, while Phantasy Star Online 2 is a game I will no doubt play again and again in the months to come.