So I think it's safe to say that these two events aren't implemented all that well. For starters, Bardle Royale is stupid since your hp and cooldowns don't reset so if you were already on at 10hp then you instantly lose (don't have a fighting chance). It's basically all built up around RNG because whichever team has the highest HP, will most likely win.
Now as for the Dueling. It's nice that the HP resets but the COOLDOWNS don't, especially for your ultimate. I also think it negatively effects it as you might have CD for your ult, but your opponent does not. I think this would be an "unfair" fight.