Initially I believe Vito saw Sollozzo as a kind of free agent asking permission of the families to set up his drug operations in New York. Barzini, who was an old time Moustache Pete was probably richer and more powerful in his earlier years, and Vito probably overestimated his wealth as well as understimated the rising power of Barzini. It served Barzini's interests to use
Tattaglia as his front man because then he could wet his beak in the drug business, increase his strength and eventually take over.