It's an old anime, from maybe 2008 or earlier.
The best part I can remember is that the main character is fleeing or something in the first episode, so he stop on a bridge, with nowhere to escape, but then he got teleported to another world. In this world, they use gems / crystals which contain monsters, and absorb their powers to fight.
This guy has a monstrous, rare, epic gem / crystal, which in legend couldn't be controlled or something. If I remember, he's yellow and looked like Greymon from Digimon. If I remember well, there's an episode where the main character fights in an arena, which reminded me of that arena city in Kino no Tabi.
It's not Deltora Quest.