Maybe I've simply doing it wrong, and while I never went rock-climbing properly, but I've been going bouldering regularly for a long time and basically... I've not felt any change except a little bit of increase in arm/hand/finger strength, but also only for the muscles used in bouldering and nothing else. Nothing for stamina or general fitness, more like doing a single strength exercise with dumbells every day.
With bouldering routes it is almost never your biceps or abs giving in, but usually the stabiliser muscles or your forearms and fingers.
So yeah, these muscles will get used and improve a little bit, but if you want to get really fit with bouldering, you need to end your session with dips, pull ups, push ups and something for abs.
Ironically, my bouldering improved immensely after switching to a workout that had less bouldering and more targetted exercise in it, and I was finally able to crack the 7c (V9ish).
Stamina is not improved by bouldering, but having stamina improves bouldering. I think some cardio just makes your body function better in every way.
Yeah I don't think it's the best as cardio. Mainly strength, and mainly in certain muscles. But if it's the only exercise you can enjoy enough to keep doing it, it's better than nothing.
