For me the Rust/Abiotic Factor mechanic is the most fun. In Rust when you hook, the fish will then start pulling the line away from the player, and also to the left and right. Your goal is to reel the fish close enough for it to be considered a "catch". The trouble comes when reeling while the fish is pulling, this puts strain on the line, and after 5 seconds or so while reeling during tension, you will hear the reeling sound get higher in pitch and eventually snap the line.
With easier fish, you can usually reel them completely in before the line snaps without much trouble, but with more difficult catches you need to time things more intentionally
You can wait for the fish to rest between bursts of pulling the line, then reel it in.
With even more difficult fish though, you do not make enough progress from reeling in-between its natural states of pulling and resting to stop it from swimming away. To counter this, whenever the fish is pulling either to the left or right, you let off reeling and "fight" the fish by pulling the rod in the opposite direction the fish is swimming in. This slowly builds up an invisible "exhaust" meter on the fish, which means while its exhaust meter is higher than its base state it has to rest more often, giving you more opportunities to reel. The exhaust meter will slowly go back down during a catch, but the fish must rest for a while before the meter starts dropping more dramatically.
This makes fishing feel like a back-and-forth game between the fish and the player, and the ways a fish will fight is pretty unique between each fish, so much so that in Rust you can usually identify the fish based on how its fighting your line. This is a very immersive experience.
Project Zomboid just has a rudimentary tension system, you have to put tension to real in the fish but too much tension will snap the line. It's quite simple, and therefore a lot less interesting than Rust's, but its still more engaging than Minecrafts. In Zomboid's case, it falls short because the fish behavior doesn't really change between fish too much, and you can usually get away with mindlessly putting as much tension on the line without it ever snapping because it's very forgiving.
A more arcade-y example would be Sega Bass Fishing. It's similar in a way but the segments in wish you have to exhaust the fish are more like QTE's rather than a dynamic system
