Maturing compost is good, I personally wouldn't use un-aged compost on anything edible due to sanitation reasons. Carrots in my experience are super forgiving, just give them whatever and they thrive. Potatoes can be a little trickier but they like nitrogen as another anon pointed out, so anything aged and mixed in sensible amounts should be fine. There's minor differences in nutrients between different animal manures but you really don't need to worry about that unless you're trying to min/maxx a commercial farm's profits or growing something really finicky.
