The question does not depend on the distance but on other factors subject to time dilation, that is movement and gravity: In short, time is passing slower for a bus driver on Jupiter than for a prisoner on Mars.
The time between the beginning of the universe and today is measured by mass particles, each mass particle may be considered as a clock. The age of the universe for massless particles such as photons would be zero because they do not experience any proper time, their clock would always be at zero. Rapid particles moving near light speed which survived since the beginning of the universe are measuring an age of the universe which is much smaller than our measurement.
Searching for an objective measurement of the age of the universe we can use space expansion which is time dependent, by referring to a reference frame which is comoving with space expansion. Earth is moving with non-relativistic velocity with respect to this comoving frame, and as a result we can consider that our clocks are (nearly) in tune with this kind of objective measurement of the age of the universe.