Yes, it all depends, a qualifier if there ever was one. Since the question sounds generic or general, I'll guess the OP is referring to regular style open iron sights rather than aperture or peep sights.
At 25 yards it wouldn't depend much on rifle or ammo as that is close enough to reduce inaccuracy caused by either to a relatively small degree. That is to say, regardless of ammo or make of rifle in themselves, most ammos and most rifles should be reasonably accurate at 25 yards.
What will affect accuracy more will more likely be on what Garaldtao refers to as the "shooting stance". If the rifle is held with the left arm extended and unsupported -- the "off-hand position" -- accuracy will be much more affected than if the rifle is held with the standing position stance used by three position target shooters, with the with the left elbow supported on the hip.
Compare the two standing positions below.
Group sizes will vary according to experience and practice and eyesight as well as the standing position used. At 25 yards with regular open or iron sights groups of one inch groups are not unreasonable. It's worth noting that whatever is achieved at 25 yards, it can easily be tripled at 50.
At the same time, with open sights at 50 yards the grouping size is a little more difficult to anticipate. Here particular ammo and particular rifle play a greater role. While some makes and models of rifles are made to shoot better than others, inexpensive bulk ammo is much less accurate than match ammo, and it will show in group sizes no matter what position or sights are used. But the greatest role remains the limitations of the sights sights as well as the "shooting stance". Groups shot off-hand groups will invariably be large although practice and experience can shrink them. Groups shot in the 3P standing position will be more consistent, but they are limited by the nature of the sights.
To see what the best groups the rifle and ammo being used can achieve at 25 or 50 yards, try shooting from a steady bench or table with a sand bag or something similar. That can help provide a benchmark from which to further evaluate results.