While they're both rhythm games with similar concepts, their purposes are very different. Beat Saber is a very fun game. Total pick up and play for anyone and great to show off to friends. Get a group together, pass everything around, and have a fun night. It's perfect for those of us who treat VR as something to share with others while still being a blast by yourself.
How much of an improvement over Box VR is Beat Saber? I enjoy Box, but I've heard Beat Saber is peak PSVR...and it's never going on sale, apparently.
BoxVR is a workout simulation that also happens to be fun. There's no penalty for failing in the normal play. You'll do workouts from just a couple minutes long all the way up to over an hour, if you so choose (and are able). This is not great for sociability, unless it's just a couple of you and you're patient with each other. But it does make working out legitimately fun.
So it kind of depends on what you're looking for. I have both and love them equally for the different reasons described above.