Superbowl

They tend to do the cat poof thing to swell up if they want to look scarier.

But they really seem apprehensive to fight due to risk of injury. Predators get driven off by small birds all the time because even though they would win in a fight, they don't want to risk anything when they could just move along. When moving is the dangerous choice though, trying to become invisible is the better choice.

Here's a video of a Screech going into a concealing posture. You can see it adjust to the width of its perch and turning to hide its lighter patches and squinting to hide the eyes. If you let it play for a bit, the next scene goes into that swelled up, aggro posture.

We also had this post recently showing the biggest owl, the Great Grey go into a similar pose and doing a decent job blending in, and it also has some potoo doing the same. Ideally they get into this position before they're seen, so while we see them due to being the focal point of the camera, if this was in an area with many trees, they'd be tough to spot.

I can't find them now, but Bald Eagles and GHO go at each other constantly. So do Harriers and Short Eared Owls. They share the same hunting areas and same food sources, so they are direct competition. The GHO even will take the Eagles nest sites. The Harriers and Shorties go at each other pretty openly, but the GHO and Eagles are exciting to watch as they will ambush each other since they're active at opposite times of day.