No, the time dilation experienced by an observer moving close to the speed of light would not be the same for both the moving person and the stationary observer. According to the theory of special relativity, time dilation occurs when an observer is moving relative to another observer at a significant fraction of the speed of light.
From the perspective of the stationary observer, time appears to pass more slowly for the moving person. This means that the moving person's clock would seem to tick slower compared to the clock of the stationary observer.
However, from the perspective of the moving person, they would perceive themselves as stationary and the stationary observer as moving at a high velocity relative to them. In their frame of reference, it would be the clock of the stationary observer that appears to tick slower.
This seeming contradiction is resolved by understanding that each observer's frame of reference is valid and relative to their own perspective. Both observers experience time dilation, but they perceive it in relation to the other observer's frame of reference.
It's important to note that time dilation effects become more pronounced as the relative velocity approaches the speed of light, and the equations of special relativity can accurately describe these effects.