It depends on your goals and preferences. If you prioritize climbing performance, it's generally better to climb when you're fresh and have the most energy. In that case, running after climbing can be a good way to incorporate cardio without compromising your climbing session. Running after climbing can also serve as a cool-down activity.
On the other hand, if your primary goal is running and you want to maintain or improve your running performance, it may be better to run before climbing. Running before climbing can help warm up your muscles and prepare your body for the climbing session. Just be mindful that running beforehand might affect your climbing performance if you're already fatigued.
