Dr. Bashir was genetically enhanced, but not in the same way as Khan was. Bashir was subjected to a very specific procedure, Accelerated Critical Neural Pathway Formation, not to engineer a superman but to (over)compensate for his slow mental development as child.
At age six, Bashir was small, not very bright, and a bit physically awkward for his age. In the first grade, while the other children were learning how to read and write and use a computer, Julian was still trying to tell a dog from a cat and a tree from a house.
The focus of his "enhancements" were to increase his mental abilities and as such, his IQ jumped five points a day for over two weeks. Further treatments led to improvements in his hand-eye coordination, reflexes, vision, stamina, height, and weight.
We know from various episodes that it also gave him a photographic memory, a resistance to Romulan mind probes (DS9: "Inter Arma Enim Silent Leges"), and the ability to consciously control many of his bodily processes, such as blood pressure (DS9: "Extreme Measures").
Since his strength and speed were presumably "normal", his parents would not have been as motivated to artificially enhance them. These enhancements would also have probably been much easier to detect, increasing their risk of incarceration.