In my opinion, this card is still too weak even with the changes Supertramp recommended. My suggested rework is as follows:
"Blue-Eyes White Dragon" + "Red-Eyes B. Dragon"
This card's Attribute is also treated as DARK. Once per turn, you can tribute 1 LIGHT or DARK monster to send 1 card on the field to the Graveyard. Then, if the selected card was a monster, you can inflict damage to your opponent equal to that monster's ATK. This card cannot attack the turn you activate this effect.
The card was seriously underpowered, so I thought that making the destruction apply to any card would make it more versatile. Plus, I changed the DEF based damage to scale off of ATK. Third, I figured that the attack-limitation should only apply if the destroyed card was a monster AND you chose to inflict damage to your opponent. Finally, I made it so you send the selected card to the Graveyard instead of destroying it; this prevents many of your opponent's counter strategies. I understand these are some large liberties I've taken, but I feel the result is a card that is atleast balanced.