Can you see the difference with the naked eye whether Venus is at the other side of the Sun or at the Earths' side?

When Venus is at an angle with the Sun from the Earth's perspective we are able to see the reflection of the Sun on Venus. But imagine that Venus is on the farthest half of its orbit around the Sun. In that case the planet is further away but we receive his reflection on a larger plane. So could an eye see the difference whether Venus is further away in his orbit or closer to the Earth?

The apparent brightness of Venus does vary. The distance and phase both affect the brightness, and the light doesn't reflect equally in all directions (though this effect is less significant than in the case of Mercury)

The maximum brightness of Venus occurs at a phase angle of 125 degrees. This is a crescent (0 is full, 90 is half lit and 180 degrees is when Venus transits the sun.)

The brightness curve doesn't vary extremely

In this image generated from NASA data by David Barry you can see the peak brightness is about -4.9. There is a short central dip. The brightness drops to about -4 as Venus gets further away (even though its phase increases) and note the small rise when Venus is most distant (due to more light being reflected directly than at an angle). These occur when Venus is close to the sun in the sky, and so the brightness can be lost in the dawn or dusk sky.

Judging the difference between -4.9 and -4 is rather difficult, especially as you are not viewing it against a dark background.

• There's a lot more about Venus' remarkably constant apparent brightness in this answer – uhoh May 19 '20 at 3:57

In James K answer, the brightness (magnitude) is used as a proxy for distance. As an answer to this question reminds us (When did people first measure that the Earth was closest to the Sun during January?), the apparent speed of an object across the sky also gives an indication of distance from the Earth. In the case of Venus, it appears to move faster just before and after passing in front of the Sun (inferior conjunction) than when it is passing behind the sun (superior conjunction). It makes sense to infer that Venus is closer to the Earth when it appears to move fast and farther away when it appears to move slow.

Another method is by noticing the size of Venus. When Venus is approaching inferior conjunction, people with excellent eyesight can see the crescent of Venus. (If your eyesight is not excellent, try making a 1/16 inch or 2 mm hole in a piece of cardboard or bottle cap, and look at Venus through the hole.) Since the size and phase can be distinguished at this time and not at other times, you can reason that Venus is closer at inferior conjunction than at superior conjunction.

Can you see the difference with the naked eye whether Venus is at the other side of the Sun or at the Earths' side?

If you have excellent eyesight, probably!

In this answer to Venus' magnitude during inferior conjunction I plot several bits of information about Venus' orbit and its relationship to Earth and visibility from the JPL Horizions database. I've added one more plot below which is the diameter of Venus' disk in arcseconds versus time. It peaks around 60 arcseconds!

According to Wikipedia's Visual acuity

The maximum angular resolution of the human eye is 28 arc seconds or 0.47 arc minutes, this gives an angular resolution of 0.008 degrees, and at a distance of 1 km corresponds to 136 mm. This is equal to 0.94 arc minutes per line pair (one white and one black line), or 0.016 degrees. For a pixel pair (one white and one black pixel) this gives a pixel density of 128 pixels per degree (PPD).

Since Venus will be a thin arc just before and just after closest approach, I think that it will be possible that it appears to be elongated perpendicular to the ecliptic rather than a fuzzy circle. So the experiment is worthy trying for those with excellent vision.

above: Phases of Venus, from here.