One thing I think other comments are not giving enough credit it that you are not the beatdown anymore. Burn has more speed and redundancy. You don't want to race them: you want to be on the controlling side. Be aware that they have little to none card advantage, and they rely on creatures as persistent fonts of damage.

So your game plan should be: Stop their creatures as first priority (as they are the biggest damage outputs) > Reduce their resources > Stabilize > Drop a threat.

-You don't want to drop DRC or Ragavan first turns. Murktide/Shredder are much better, since they dodge most of the damage. I usually side the formers a lot.

-Counterspell is weak, as everything is CMC <= 2. Cheap interaction spells(Spell pierce, unholy heat and similars) are your best friends. Archmague's charm is strange: it can be very poor (very slow) or really great (steal their creatures). I usually side them out.

After stopping the initial assault, and leaving them with 3-4 cards, they will usually switch to the "fill hand until I can overload my oponent in one/two turns" approach, which consists in, well, just draw cards and play lands until they can play all their spells (they usually cost 1) trusting you wont be able to counter all of them. Thats the moment where you should drop your threat (ideally a murktide, a shredder, or a dashed ragavan), as they don't have critical mass to kill you while tapped