Difference between sunrise and sunset?

In real life: A sunset is "redder" than a sunrise which makes people feel more romantic.

It's mostly because the atmosphere is warmer in the evening (no pollution here, lemon, the Earth is warmer in the evening because it was naturally warmed up during the day). However, there's also a very small contribution of the Doppler shift, one that you could in principle measure accurately. When you're looking to the East, your point on the Earth is moving towards the Sun at speed up to 1,500 km/h or so (on the equator). This small velocity still exceeds the radial component of the velocity around the Earth, I think, so if you measure the Doppler shift accurately, you may learn something about the motion.

You may also watch where the Sun is moving. If it is setting (dropping, approaching the horizon), it is a sunset, and if it is rising, it is a sunrise. ;-)

I don't know if this is kind of answer you're looking for, but you could measure the temperature difference between the air and the open ground (as dark as possible). Over the course of a day they should diverge because the ground absorbs so much more radiant energy than the air. By sunset they will have equalized some, but by the following sunrise they will have equalized even more, because at night there's almost no radiation to make up for the heat the ground loses to the air and sky.

Of course weather might frustrate this test.

You got other answers explaining that there are physical reasons in the atmosphere for a sunset to be slightly different from a sunrise. But the problem is that the variations from one day to the other in atmospheric vertical profile (temperature and water vapour) because of meteorological effects are IMHO much greater than the difference caused by the day heating. So if you have only a visible photography, the signal/noise ratio will not allow you to certainly determinate. You would need more informations to deduce the vertical atmospheric profile and from there the moment in the day