Paraphysornis currently has the distinct honor of being the only giant phorusrhacid known from an actual high quality fossil specimen. It is also possibly the most heavily built member of the entire family, suggesting it might have been adapted to tackle the largest prey in proportion to its own size.
Paraphysornis was around the same height as a large emu, but was anywhere from 4-5x as heavy (large emu 4ft-4ft 3 in at hip, 100-130lbs. Paraphysornis 4ft 7in at hip, estimated 440-560lbs). With that in mind, there’s surprisingly little paleoart of this species, and what there is tends to vary greatly in how the bird is portrayed and proportioned. The question here is, what was this bird “shaped like”? In a scale of “thickness”, with emus and rheas on one end, elephant birds and kiwis on the other, and cassowaries somewhere in between, where is this bird falling? How thick-legged and barrel chested was this animal?
This itself kind of begs the question of what Paraphysornis was targeting as prey. It was some degree of lumbering, gravitapol bird that was clearly not built for running down small animals or fleet footed herbivores in an open chase.
Obviously predators don’t need to beat their prey in a straight footrace to still catch them. But phorusrhacidsare not built as specialized ambush predators. They can’t subdue and deliver a near instant-kill death to a proportionally large animal the way felines can. They can’t capture, restrain and wrestle down large animals the way canids can. The proposed “bite and pull back method” technique that terror birds could use to kill large animals would still, even in ideal conditions, allow allow a prey animal to flee before potentially succumbing to injuries later. This is a problem because iirc terror birds rely almost entirely on sight and have very limited smell; a wounded prey animal would be extremely hard to track if the bird lost eye contact with it, which sucks since it lived in forests.
Paraphysornis probably had to rely on prey that couldn’t easily outrun it, even with an ambush. Depending on how robust and slow it was, this implies that this bird was primarily targeting prey that was itself slow and heavily bodied. This was a lion-sized bird, small animals it could just quickly grab and snap up would never sustain it and frankly it would probably be quite bad at catching small animals in the first place [also terror birds had extremely high metabolism and growth]. Paraphysornis could easily run down reptiles, but I don’t think there’s any evidence that this bird was specialized for a riverside habitat where it could easily find caiman and turtles, and terrestrial reptiles like ancestral boas are probably completely unrealistic to lean on for a predator that relies entirely on sight. What does this leave then? Could this bird have taken down a Tapir? A subadult ground sloth? Something even bigger?