I think both are great and offer very interesting prizes, but in terms of said prizes, I like what the Fishing Tourney has to offer more, as I actually use several of these around my island as decor, such as the Anchor, Fish-drying rack, Fresh Cooler, Fishing-rod stand, and the very adorable fish pochette for me!
The only Bug-Off item remotely useful as decor imo is the Artisanal Bug Cage, but I have to say that out of the two NPCs, I enjoy Flick a lot more in terms of design and dialogue. I'm fond of reptiles and I just think his obsession with art and bugs is so entertaining
C.J. has his fun moments too, but he's more millennial whereas Flick is a bit more traditional which I tend to like more.
To me, the Fishing Tourney feels more like an actual sport, where it's you vs. the timer, using fish bait, finding the right locations to fish, casting the line properly and working hard for them fishies, and with the Bug-Off it's more like an adventure/expedition, running around swinging your net. Bugs can spawn more often around the whole island, yes, but that's only when you're not actively hunting them down lol at least, in my experience. When I couldn't care less about them, they're all over the place buzzing around my face and around the gardens, but when I really need them the most it's like they become extinct.
While I do enjoy fishing because you never know what you'll catch and I like that element of surprise and challenge, those fake bites can get pretty annoying pretty quickly, especially when you have a timer on your back (my cue to press A is the splash sound that accompanies the actual bite, and it helps if I close my eyes to listen) I also really like the more carefree nature of bug hunting, so I have to go with the Bug-Off. But the Fishing Tourney definitely offers the better items.
I honestly would have liked both competitions way more if it were like in New Leaf where you could win items from the Insect Set (such as the Cicada Stereo and Caterpillar Sofa which were so amazing!) and the Fish Set (the Red Snapper Chair and Puffer-fish TV, just wow!) It would have given me much more incentive to participate in these events more often.