As a baseball geek, I will tell you that you can ask a million questions about this stuff and not get the answers you want with the vagueness in this thread. What age batter? What experience level? What kind of bat?
Bat speed would be considered swing analysis. This is where you get mph of the bat head, time to impact, etc. This is about swing mechanics. Check out Zepp. They have a lot of software and devices in this world. I am sure you can read up on it or watch videos of their systems to learn more.
Exit velocity is an after contact measurement. It's a radar based tracking of the ball with the same system usually that tracks the pitch. Exit velocity is not just a measurement of swing speed, but also the quality of contact or hitting the sweet spot. Trackman makes the systems used in MLB. They can also measure launch angle and spin rate which will provide data about swing path. Check Trackman out as well.
In summary, exit velocity is a measurement of results based on everything leading up to contact. Swing analysis is going to allow you to break it all down prior to contact. If the end goal is game improvement, swing analysis is going to help figure more stuff out that can help.
Exit velocity is just going to put data on what you can see with your eyes. How high, hard, and far will the ball travel. Scouts want the Trackman data. Coaches want the Zepp analysis.