I usually choose Fruit Bats, by doing so you are able to submit some of the fruits needed for some of the bundles (Enchanterer, Fodders, Artisan, Summer Foraging, and Fall Foraging) at the Community Center without having the need to plant the trees—you might also be able to complete the Community Center by the end of Year 1. You are also able to utilize these fruits by placing them into jars and kegs.
In addition, the star quality of these fruits also increases as you level up your foraging level. You are able to achieve this by choosing Gatherer (At Level 5, Chance for a double harvest of foraged items.) and then Botanist (At Level 10), by doing so, all of the foraged items will be a high star quality such as iridium star.
However, choosing Mushrooms is just equally helpful in completing the exotic foraging bundle. You are able to utilize the mushrooms into creating Life Elixirs, which give 200 energy and 90 health. Life Elixirs are quite helpful if you go to the Mines and Skull Cavern often.
Overall, I would still prefer on choosing Fruit Bats since it is quite versatile when it comes to its usage. Not only that it is quite helpful for the community center, but it is also helpful in earning money by shipping it directly to the bin or by placing it into jars/kegs to profit more. However, if you're more inclined toward Mushrooms, then it is also alright since it provides an increase in health when crafted into Life Elixirs. To be honest, it's just a matter of preference.