In terms of pure speed, in their respective universes, the Flash (Barry Allen) is faster, by far, than Quicksilver .
When Marvel and DC have had crossovers between Universes, Quicksilver's powers remained constant due to their mutant origins (which presupposes his body has been organically adapted for the use of superhuman speed)
while the Flash's speed is an aspect of an external power which he may not have access to in the Marvel Universe.
With great effort, the Flash may reach the speed of light, in atmosphere, without deleterious environmental effects!
Quicksilver has been seen at a top speed of four or five times the speed of sound (Mach 4 or 5).
This level of speed for Quicksilver is new.
He used to max out at Mach 1.
Since crossover events are exceedingly rare, it is safe to assume that if you were comparing their speeds, the Flash is consistently faster than Quicksilver, though operationally speaking both could be consider comparable since their feats tend to be done at the same overall speed.
Generally speaking, the Flashes of the previous DC Universe continuity were far faster than almost anyone else in their universe with superspeed because they are able to channel a temporal phenomenon called the Speed Force.
Other speedsters haven't had as pure a connection and as a result are only a fraction as fast.
See:
Johnny Quick , Jesse Quick (Chambers) , Max Mercury
In the New52 universe, Barry Allen appears to be the only Flash on Prime Earth with a connection to the Speed Force.
The renewed Jay Garrick on Earth 2 is now receiving his power from the god Mercury and does not (as far as we currently know) utilize Speed Force energies.
There was a version of the Flash on Earth 3 called Johnny Quick whose powers were the same as the Flash's of Prime Earth.
He is now deceased.
UPDATE:
To answer a question regarding both of these speedster's thinking capacities: Both have shown they are able to use their minds faster than an ordinary human.
Given their need to have increased perception abilities to handle their bodies moving far faster than any ordinary human's.
If they were unable to speed their cognitive abilities they would likely die once they were moving faster than about two hundred miles an hour because they would be limited by their human reflex time.
There is already a question here answering Barry Allen's (The Flash) ability to think at superhuman speed.
Given Barry's far greater speed, he would also likely need to be able to think at a far faster rate than Quicksilver.
Baring that, he would at least need a reaction time far greater than Quicksilver's in order to control his much higher top speeds.
See:
Can The Flash See the Future Now?
scifi.stackexchange.com/users/2765/Thaddeus Howze
Depends on the universe.
In DC, Flash can beat the speed of light while Quicksilver tops out at Mach 4.
However, in the crossover events, we've learned that Flash cannot access the speed force in the Marvel universe and cannot go faster than Mach 1 while Quicksilver has the same speed in either universe.
Source
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The below image is a common image macro / meme used to address Flash's reaction time and speed.
It is taken from the post-Crisis pre-New52 era Superman story arc "Grounded" (part 7, Superman Vol.
1
No. 709)
wherein Superman walks across America reflecting on his relation to it and, at one point, asks Flash (Barry Allen) about what he sees.
There is no explicit proof that such continuity is preserved in the current line except for Grant Morrison's Multiversity project and his position that: “People have this idea of canon, but there is no canon,” he says.
“To me, it’s all real.
Every comic you ever read is real.”
Arguably a philosophical position, but distinguishable as he is an architect of the DCU with the ability to actively shape its continuity.
Nonetheless, it is instructive in the creator's perception as to the magnitude of Flash's speed as conceived of by J. Michael Straczynski, written by Chris Roberson, and vetted by Eddie Berganza.
Such sentiments have carried into the New 52 with feats such as these: By comparison, Quicksilver is generally perceived as a super-sonic, rather tha super-luminal, speedster.
The most notable exception is when exposed to the Terrigen Mists which enabled him to time travel and create temporal duplicates of himself.
However, the ability took a severe toll on him and such abilities are commonplace to the Flash family.
Impluse (Bart Allen) similarly had temporal duplicates and several iterations ofthe Flash and members of the Flash family can time travel.
Thus, Flash is consistently portrayed as faster by an order of several magnitudes.
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Which flash are we talking about?
The Barry Allen flash is technically the fastest thing in both universes [1] .
In terms of his max speed, he can "run faster than the speed of thought" [2] (which is a really weird way of saying hes infinitely fast).
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Flash (BARRY ALLAN)
In Flash #150, "straining every muscle," he ran at ten times the speed of light.
And lets see this pic - Death of THE FLASH
HE IS THE FASTEST THING IN ALL UNIVERSES full size of pic: http://img4.wikia.nocookie.net/__cb20121005105640/marvel_dc/images/5/57/Flash_0050.jpg
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We see a lot of information about both of them, but is there a specific speed that each one can reach? I'm trying to figure out the current speed of each one, in the current comics line.
Who's faster? Quicksilver or Flash?
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<marvel><dc><the-flash><quicksilver>
scifi.stackexchange.com/questions/67581
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In Flash #150, "straining every muscle," he ran at ten times the speed of light. Quicksilver has been seen at a top speed of four or five times the speed of sound (Mach 4 or 5). Flash is faster. Flash may reach or surpass the speed of light and Quicksilver is known to run at a speed that far surpasses the speed of sound. 
Flash may reach or surpass the speed of light and Quicksilver is known to run at a speed that far surpasses the speed of sound. 