Faster? yes, better reflexes? i doubt that.
Spiderman is at most 15x human reflexes, DS is around that too probably 10-15x but has shown to be far more capable at using his reflexes. Remeber he shot impulse twice, once while he was running at faster than sound.
Spiderman isn't going to be able to dodge a bullet/plasma blast when it's being fired by someone who is on par or above SM's reflexes.
Remember, punisher shot him a few times.
The dexterity is up for debate as well, while SM is more agile, he isn't very far above DS. In batgirl #63 DS was said to be moving like a high speed dance with each move 12 steps ahead of the other. (bouncing off the walls and doing crazy weird agility type things)
A series of punches and kicks could take DS out, but SM simply isn't good enough fighter to do this, DS is basically on of the top 3 DC martial artists. All DS needs is a choke hold/ nerve punch.
Add all this to his 10x intelligence and DS will out strategize SM and out fight him.