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Are there any quotes stating Vader is quicker than Anakin or vice versa?

I don't think so. Both have great hype about their speed, but not in comparison to each other, at least not directly. There is an implicit indication made, however, through Yoda acting as a measuring stick, that Anakin Skywalker as a Jedi would be faster than Darth Vader.

This is Anakin Skywalker:

The most powerful Jedi of his generation. Perhaps of any generation. The fastest. The strongest. An unbeatable pilot. An unstoppable warrior. On the ground, in the air or sea or space, there is no one even close. He has not just power, not just skill, but dash: that rare, invaluable combination of boldness and grace.

He is the best there is at what he does. The best there has ever been. And he knows it.

Revenge of the Sith novelization

It happened before he could get out another word. Faster than an eyeblink. Faster than he'd seen anyone move, anyone except Yoda.

Last Of The Jedi: Secret Weapon

In the above, both Anakin and Vader are compared to Yoda. Anakin is lauded as the fastest Jedi of any generation, which would include Yoda, making it an indirect comparison between the two, and having Anakin as superior. In Vader's case, it is more direct, and he is explicitly stated to not be faster than Yoda. If Anakin is faster than Yoda, but Vader is not, then Anakin must also be faster than Vader.

One should not however, that this is Vader only a year after acquiring his suit. His exponential growth throughout the following decades has been greatly explored upon in the realm of telekinesis, lightsaber combat, and overall combative viability, though not in speed. It would make sense for him to grow relatively evenly across all areas of the Force, although there is no explicit confirmation. Whether Anakin is faster than peak Vader therefore comes down to one's own subjective interpretation of the source material.

Pablo Hidalgo's Head-to-Head:

Agility (out of 10)

Yoda: 8
Sheev: 8
Vader: 4
Anakin: 9

Originally posted by Kurk
Pablo Hidalgo's Head-to-Head:

Agility (out of 10)

Yoda: 8
Sheev: 8
Vader: 4
Anakin: 9

agility isn't speed though...

http://www.dictionary.com/browse/agility

Agility is a specific type of speed

speed is involved in the combination of attributed needed for great agility but it isn't pure speed. Agility is the ability to change the body position efficiently... completely different quality than raw speed