The Flash is the speedster from the DC Universe, while Quicksilver is from the Marvel Universe.
For starters Flash technically is a human who got his powers in an accident on the other hand Quicksilver is a mutant, which basically means he is born with those powers.
The Flash (Barry Allen) is a part of the Justice League but when it comes to superhero team affiliations Quicksilver just has a crazy amount of them, like he is the part of Avengers, Inhumans & Brotherhood of Mutants among many others.
Flash is granted his power by something called the speedforce which give all the speedsters like him in the DC universe their powers, Barry Allen is the first Flash out of the the many, like Wally West but what makes Barry unique is that he is the origin of the speedforce. Whereas Quicksilver is a mutant, so he doesn’t need any source to power him.
The Flash can run the the speed of light while Quicksilver can run at the speed of sound which makes Flash the fastest. While many may argue that Flash relies on speed force for his powers but in The Flash: Rebirth #4, Max Mercury revealed to Barry Allen that the Speed Force was created by Allen, himself, when he became the Silver Age Flash; adding that, “When [Allen runs, he generates] the kinetic wall between the present and the time barrier. It’s an electrical energy that exists in every dimension, every universe, and every era. It touches every part of reality. It contains the knowledge of every place and time. The Speed Force is the all-encompassing Flash Fact.”
In the JLA/Avengers crossover it is depicted that Wally West is unable to use the speedforce in the Marvel Universe as a result of which Quicksilver defeats him easily but the case with Barry Allen is different.
Well, while fighting you just can’t run and dodge the bullet but you need to fight back or eventually, you will fall.
Talking about abilities, both Flash and Quicksilver have unique set of abilities.
Starting with Quicksilver, he has superhuman strength, good fighting skills, better resistance to attacks and molecular destabilization which basically allows him to destabilize atomic matter by accelerating its molecules often causing it to fall apart or explode.
Flash has the ability to heal faster, use his brain faster, he can pass through objects, and has increased senses. I know you can say that even Quicksilver can think faster but c’mon Barry is a forensics scientist, who do you think will perform better?
Both the speedsters can travel back in time but both have different ways to do so.
So comparing both of them on the basis of ability is a tough choice but here’s a catch, if Flash channels all of his energy in a one single punch he can even knock down Superman but Quicksilver has better fighting skills, so if he somehow misses that punch he can still pull a decent fight.
Now that we have talked about powers, lets talk about how they are presented, as far as the origin goes, Quicksilver surely has a deeper story, probably because he is the abandoned child of Mangneto. Flash does better when connecting the timelines of the past and the present both have better villains. It can be also said that Quicksilver has a darker story when compared to Flash.
It surely is tough deciding the who is a better speedster, both Flash and Quicksilver are unique in their very own ways. If I were to choose, I would definately go with Flash.