There is not a lot of difference. The numbers just tell you how much of each element is present. Since the ratios are the same, it just takes a little less 13-13-13 to provide the same nutrients as 10-10-10.

Another thing to pay attention to is whether the fertilizer is "slow release."

Nate

Use the 13-13-13. It will do as well as the 10-10-10. I think it is just that the 10-10-10 is more commonly available. At least around here it is.

Someone in Florida, growing their plants in sand or potted, may need a 10-10-10 fertilizer, but this ratio is rarely a good thing for more common soils. I commonly use 13-13-13, but only in potted plants. I suggest getting a soil test before using such a fertilizer. The fertilizer ratio I have most often seen recommended for daylilies is 3-1-2. This should be adjusted, based upon your soils needs. Over applying some elements can cause toxic conditions.
Ed

Ed I have put 10-10-10 on my daylilies. Just do not use too much.