In Titan, everyone has to dodge. DRG get a little more leeway due to more HP, but its not much. If anything, BRD are going to be dodging more since Plumes like Ranged for some reason :/

However, DRG have many more AoEs to deal with normally (outside of Titan) thanks to them being melee. And they are positional DPS, so you do need a bit of precision and positioning to do well.

BRD are overall easier, but are definitely more boring than DRG.

Why not level both to 15 or 30 (you need to level LNC to 34 for BRD as it is right now, and until the patch notes say otherwise assume you still need BFB as a BRD after the patch), run some dungeons as each, and then decide for yourself?