Part of the answer to this question has already been answered in depth in another post. As to exactly how close he is to Khan, it's conceivable that since the process Bashir underwent as a child, was to (as was stated in the link) compensate for his slow mental development, it did not affect Bashir in the same way. Bashir was genetically modified as a child to compensate for a deficiency, where as Khan and many others from his time were a product of the Cold War, which lead to the Eugenics Wars. Khan and his people were genetically bred to be the best at everything, both mental and physical.
After the Eugenics Wars and World War III, genetic engineering was banned.
Genetic engineering of Humans was ultimately banned on Earth, as the concept was considered anti-Humanistic by Earth leaders. As a result of this, Doctor Stavos Keniclius was exiled from his community, which eventually led him to depart Earth permanently. The ban was placed primarily as an attempt to prevent another event like the Eugenics Wars, and to ensure that Humanity did not endure the wrath of another Khan Noonien Singh-type tyrant.
(TAS: "The Infinite Vulcan"; DS9: "Doctor Bashir, I Presume", "Statistical Probabilities")
In Bashir's case, aside from finally having to come clean about his enhancements, things turned out well for him. Admiral Bennet recognized, regarding Bashir, that good can come out of enhancements such as these but the overall danger of using such enhancements still exists.
"Two hundred years ago, we tried to improve the species through DNA resequencing. And what did we get for our troubles? The Eugenics Wars. For every Julian Bashir that can be created, there's a Khan Singh waiting in the wings – a superhuman whose ambition and thirst for power have been enhanced along with his intellect. The law against genetic engineering provided a firewall against such men.
(DS9: "Doctor Bashir, I Presume")
To my knowledge it was never specifically talked about as to how strong Khan specifically was, but the the general average of an augmented human has been.
Records of the period, including Khan's origins, are fragmentary and therefore vague. He was the product of a selective-breeding and genetic-engineering scientific program, based on the eugenics philosophy that held improving the capabilities of a man improved the entire Human race. Augments produced by the program possessed physical strength and analytical capabilities considerably superior to ordinary Humans, and were "engineered" from a variety of Earth's ethnic groups.
Records from this period are fragmented, but what is known is that the wars' roots lie in a group of Human scientists' ambitious attempt to improve the race through selective breeding and genetic engineering. They created a race of "supermen," popularly known as the Augments, who were mentally and physically superior to ordinary men and women. They were five times stronger than the average person, their lung efficiency was fifty percent better than normal, and their intelligence was double that of normal Humans. They also had enhanced senses, including an ability to hear beyond that of Human capabilities.
(TOS: "Space Seed"; ENT: "Borderland", "Cold Station 12")
The answer you are looking for would conceivably be that there is no actual percentage. The differences between Bashir's enhancements and Khan's vary greatly. Bashir was enhanced using the process called Accelerated Critical Neural Pathway Formation, whereas Khan is a combination of genetic engineering and selective breeding which would allow for the best of all physical characteristics to be bred into a person, then genetically enhanced. As far as mental capabilities go, it is possible that Bashir was on par with Khan, but seeing as how the enhancement was only a mental enhancement, Khan was vastly superior physically.
All links, quotes and episode references were taken from Memory Alpha and another post regarding genetic enhancement