If you want to keep flexibility and avoid tethering yourself to either AirPlay or Chromecast, you can still have both depending on which platform you use. Great part is that this works seamlessly with just a few minutes of setup and then you're set to mirror any device - smartphone, table, or even a supported computer.
Some apps won't likely due to security protections, but a good number of games can be played from your mobile on the bigger screen (expect some lag).