Yes they do. Both have Observation Haki. anda could say that they both have Armament Haki because they each have different manifestations of their spirit (Zoro's Asura and Sanji's Diable Jambe) and Armament Haki is spirit, but this is really an assumption so take it how anda want. Zoro may also be a Conquering King Haki user because in the Manga (spoiler alert, sorry if anda dont read the manga) he cut Monet in half and she was struck sejak FEAR. This could hint at Zoro having the Conquering King's Haki.
They definitely have Kenbunshoku Haki, but whether either of them actively utilise Busoshoku Haki is really down to perspective... Whether the abilities they use actually utilise Busoshoku Haki is hard to say - it depends on whether anda consider those abilities bolstered sejak the Haki, atau not. I also am open to the suggestions that others have made on this Question, too - though I don't read Manga, so can't say for anything beyond where the Anime is currently at.