Most modern solid-fuel rockets use pretty much the same fuel as the shuttle SRBs. It's cheap, stable and reliable but it does produce a lot of goop and the ISP could be better. If this stuff is stable it might make an excellent replacement for ammonium perchlorate oxidizer.
Shuttle SRBs are more expensive and less reliable than equivalent liquid boosters. This is the main reason why SpaceX is only using liquid engines in the Falcon-9. ULA uses solid boosters for extra thrust on the Atlas V, but these solids are cheaper and more reliable than Shuttle SRBs. In addition, based on recent conference papers, I think they want to get away from solids in their next generation of rockets.
So why is NASA planning on using boosters based on the lower performing, more expensive, and less reliable Shuttle SRBs in their new Heavy lift rocket? This is because the Utah Congressional delegation is lobbying heavily for the company that makes the SRBs. The Utah senators inserted text into the continuing resolution that NASA is currently operating under that they claim prevents NASA from even doing trade studies to consider any alternatives to using the Shuttle SRBs.
Solids might have made sense in the 60s, but with current technology they are no longer needed except in a few specialized applications for robotic planetary exploration spacecraft.