Yes there is a different taste between them. Cider vinegar has a more mellow, milder, sweeter flavor. White has a sharp, more acidic flavor. It's a bit more dominant in taste. Some prefer one, others prefer the other.

Personally when the color isn't important in the appearance of the finished product, I much prefer cider vinegar for pickling, especially fruits. But you need to try both and see which you prefer.

Dave

In general, I prefer white vinegar for pickling savory, and cider vinegar for pickling sweet. This is more to do with the other seasonings in the brine rather than if it's a veggie or a fruit. But since fruits tend to sweet, I tend to use cider more for those recipes.
There is for sure a big taste difference between the two. Different in the fresh form, and matures to different final taste too IMO.

I went ahead and pickled some loquats in Apple vinegar. The white vinegar is a little stout.