I chose fruit bats my first playthrough, and mushrooms the second (current) time around.
As mentioned by others, the fruit path is great for the community center. What I looked forward to with mushrooms was being able to make life elixirs pretty early in the game. But the relative scarcity of the purples (or really, anything besides "common mushroom") didn't lead to a steady stream of elixirs.
Another difference between the two is that you're limited to six boxes to harvest mushrooms from, whereas the limit for fruit seems to be some percentage of the total number of tiles in the cave. However, the spawn rate of fruit seems to be less than the six per day you get of mushrooms. So if you're good about consistently checking the cave every day, mushrooms may be the better option. But if you're like me and only get around to the cave every few days (or over a week), fruit may be more suitable to your play style.
Other differences (as I discovered on the wiki):
- fruit gives you foraging xp; mushrooms do not
- fruit is universally liked, whereas mushrooms are kind of a crapshoot - ~3-5 villagers like each EXCEPT everyone dislikes or hates reds and one love
Later in the game, I don't think it matters very much - you'll have established friendship with all the villagers and your cash flow and growing capability will be enough such that you can cook food or buy elixirs to heal yourself.
Thinking about it, I think ConcernedApe did a really good job of balancing the two options. If there was a poll, my guess is that the fruit would win for giving you a jump on the community center bundles. But I definitely would not fault anyone for preferring mushrooms. To me, mushrooms are the more interesting option for the long-play, for the somewhat steady influx of the rarer fungi. Not that I would
need them for anything, but just because I'd already be getting the non-foraged fruit from trees.