Battery box idea for my project
It's hard to say which is better for you without really being able to examine your trike there. I like to use a couple layers of heat shrink, oriented 90 degrees to each other. That way all six sides of the battery are covered. It's not 100% waterproof, but it's pretty splash resistant that way. Make sure however you mount the battery, the wires exit down towards the ground. That keeps gravity from feeding water into the back along the wires.
A hard case enclosure can be potentially more waterproof, if it has good seals and gaskets. But depending on the size and shape of your battery, it can be hard to find an off the shelf solution. For a trike that powerful, you'll likely want a big battery anyways.