One of these things is a weapon that is used for combat. One of these things is an object used while playing sport.You’re asking about an improvised weapon versus an actual weapon. In that, the actual weapon has the advantage.
While a baseball bat can be devastating if it connects, there are too many ways to circumvent it. The heavy tip means that when it’s swung it creates a wide arc, but all the force is in the tip. An unarmed fighter can completely dismantle a baseball bat’s effectiveness by getting inside it’s arc, because of the way the force is distributed it won’t actually do much damage if the target isn’t in the right place. It’s also painfully easy to avoid because the swing is so large. You can test it’s effectiveness, actually, if you have a baseball bat at home. Take it out into the yard and swing as hard as you can, then try to bring it back. How long does it take for another strike if the first misses? The answer is too long
A baseball bat is very dangerous to someone who is untrained and doesn’t know what to do with it or someone who is already prone on the floor.
To turn a baseball bat into a useable weapon, you have to grip it about halfway up the length of the bat. However, while it becomes more effective as a defensive weapon, it greatly reduces it’s range thus lending the sword the advantage.
A better match up, ultimately, is a sword versus a tire iron. The tire iron can be wielded like a baton or nightstick and will damage the edge of the sword when it connects. The wielder of the tire iron will have no fear going after the blade itself, because the tire iron is the more durable of the two. The person wielding the tire iron is still likely to lose, but it’s ultimately more interesting.