Barn owls (at least the ones most of us think of) are medium sized owls. This is a Tyto alba, a Western barn owl, which averages 13-14 inches / 33-35cm and a weight from 400-700 grams. The Tasmania masked owl is the largest barn owl, and is maybe 25-50% larger.

Kestrels are about the same size in length and wingspan, but are 150-250 grams, so in that regard, they are much smaller than a barn owl.

Here is a thumbnail for a nest cam video of a female kestrel attempting a raid on a barn owl nest. This is a female kestrel fighting the male barn owl. With raptors, the females are around 25-30% larger than males on average, so this is a larger kestrel vs a smaller barn owl and I think the width of the barnie is pretty visible here.

If you watch the clip, the owl doesn't have too much difficulty maintaining physical control over the kesterl. There's no visible gore in the video, though the description notes the kestrel was injured. It goes choppy when the owl really tries to put the hurt on the kestrel, so you can mainly just see them wrestling.

With a snatch and grab like in the original post photo, the kestrel should be at an advantage with its speed and agility advantage over the owl.