You should really go with the manufacturer’s instructions for this one. While you can do both, doing it the recommended way will increase the durability of your board. This means that some are better to deflate completely, while others can be left partially inflated.
After a paddleboard adventure, you should always clean it, and then dry it off. If you choose to leave it inflated, never leave it with high PSI. Also, always store it away from the sun and harsh weather conditions, since these can damage the structure of your inflatable SUP.