Medieval longswords are useless compared to rapiers

There's several things to consider. Most importantly, penetration: obviously the rapier is phenomenal at penetration, and is quite long (always a positive thing). However, while some rapiers can be quite stiff, others are too flexible and floppy for proper thrusting, which can lead to embarrassing situations. A flaccid sword is a sad thing indeed. The longsword is usually thicker than a rapier - some are quite girthy - and this can help make your weapon much stiffer, which obviously helps enormously when you're trying to stick your sword deep into someone's body. That said, there are some longswords that suffer from a lack of rigidity, to their owner's great shame.

All that said, it's not always about what kind of weapon you have, it's how you use it.