Do you have any data to show how good it is for Pico488 to bind the dsDNA than the ssDNA?

In fact, Pico488 (also available as Pico488 DNA quantification kit) is designed to quantitate the dsDNA (see constants compared to SG and EB in the article published by Dragan et al., 2012). It is considered that quantitation with Pico488 is tolerant to ssDNA, but we don't have the exact constants for binding between ssDNA-Pico488

There is the reference below about the interaction of Pico488 with ssDNA:

Nakayama et al., 2016  (S1 Fig. Standard curves of single-stranded DNA quantification)