In the anime, it has been stated that "Blue-Eyes" represents power while "Red-Eyes" represents potential.
"Blue-Eyes" Decks aim for a field control strategy, usually by destroying opponent monsters. They can Synchro Summon monsters such as "Azure-Eyes Silver Dragon" to lock down the opponent's field or help Summon stronger monsters and set up a Fusion Summon for a finishing move.
"The White Stone of Legend" needs another effect to discard it and be able to use its Graveyard effect. Whereas both the Monster cards "Master" and "Sage with Eyes of Blue" have effects to Special Summon any "Blue-Eyes" Monster from the Main Deck by either "Shuffles itself from the Graveyard to the Main Deck" ('Spinning to Deck' for short) or Discards itself.
"Dragon's Mirror" is recommended for the Fusion Monster "Neo Blue-Eyes Ultimate Dragon". While it is the only face-up card you control, it can attack up to three times in the same turn by sending other copies of a "Blue-Eyes" Fusion Monster from the Extra Deck to the Graveyard. By sending extra copies of itself to the Graveyard, they will be there to protect any "Blue-Eyes" monster(s) from being targeted by effects by banishing themselves.
You can also use Trap and Spell cards that support LIGHT attribute monsters as virtually every Blue-Eyes monster is a LIGHT monster with a fewexceptions. Spell cards such as "Shine Palace" can support LIGHT monsters beyond Blue-Eyes or Dragons. LIGHT monsters such as "Honest" can easily boost the ATK of your already powerful dragons. Cards such as "Beckoning Light" and "Light of Redemption" can return your destroyed or banished Blue-Eyes monsters to your hand.
Since most Blue-Eyes monsters are LIGHT-Attribute, DARK-Attribute or Fiend-Type monsters can in-general, negatively affect LIGHT monsters, and to the worst extent, the anti-LIGHT "Ally of Justice". "Light-Imprisoning Mirror" can be devastating to "Blue-Eyes" monsters by negating their effects. Cards like "Leeching the Light" and "Sword of Dragon's Soul" (due to the "Blue-Eyes"s' monster Type of Dragon) can destroy even your strongest monsters.