For most riders, hydraulic disc brakes are absolutely worth it — and that's why they've become the standard on virtually all new road bikes above entry level. They deliver significantly better stopping power and modulation (how smoothly you can control braking force) in both dry and wet conditions, which inspires confidence on fast descents and in traffic alike.
Beyond raw braking performance, hydraulic disc brakes unlock a major practical benefit: wider tire clearance. Since the brake caliper mounts to the frame rather than the rim, you can run tires 28mm and wider, which is a huge advantage for comfort, grip, and versatility on rough roads. Rim brakes typically max out around 28mm.
The trade-off is a small weight penalty compared to rim brakes, but for everyone except weight-obsessed racers chasing every gram, the performance and safety gains far outweigh that concern. Modern hydraulic systems are also reliable and require less day-to-day adjustment than mechanical disc or rim brakes.