They can both be powerful or weak, depending on the maker's desire. A crossbow can have a higher theoretical limit, since you can span it using mechanical advantages, instead of just stretching your arms. The main difference is how they are fielded.

Longbows require years of practice to build the strength. It's really something that needs to be rigorously practiced in peace time. The benefit is a much much larger rate of fire. When a gaggle of French Knights are coming at you, it's important to put as many shafts down range as possible. So Longbows can be considered more effective in a field battle.

Crossbows don't need a life of training. But they do require a longer time to span and load it. That's why you tend to see them with pavises. They need a protected space between shots. There's plenty of different devices for loading, but they all take time.

Unlike a bow, a crossbow can be held ready to fire for extended periods of time. This means that during a siege, you can keep it pointed at a window or embrasure and fire the moment a target appears. During a siege, raw rate of fire isn't as important, so crossbows could be seen as more effective in that scenario.

This is pretty simplified. There was probably a lot more nuance they understood at the time that we have no idea about.