I know that 各式各样 = 各种各样, but is one Taiwanese version of the other one? What I mean is: is one more frequently used in China and the other is more frequently in Taiwan?
各式各样 VS 各种各样
To this mainland speaker, they are not entirely the same. Both are common and we can't say one is more common than the other.
各式各样 is about the differences in 样式, while 各种各样 the differences in 种类. In other words, with 各式各样 we see all types of things within one category. With 各种各样 we see different kinds/categories of things.
Colloquially, sometimes they might be used interchangeably. However, native speakers do feel the nuance between the two.
One crude method for testing Taiwanse vs. Chinese usage is by running a verbatim
Here are some results:
各式各样 site:.tw about 761’000 results
各式各样 site:.cn about 24’100’000 results
but maybe Google isn't good with sc vs. tc:
各式各樣 site:.tw about 12’300’000 results
各式各樣 site:.cn about 315’000 results
There doesn't seem to be much of a difference in usage amounts overall.