There are so many flatwound string brands available now that it can be a little overwhelming. In general all flatwounds will give you a warmer, more mellow tone than roundwounds but there are differences with each brand.
Although the basic design for flats is the same, there are several small differences in the construction of the string that can have a large impact on the tone and feel of each flatwound string set.
While roundwound strings are still by far the most popular bass strings, flatwounds have seen a huge resurgence in popularity within the last 10 years. As a consequence there are now many more choices for flats than ever before.