It's obvious to me that Cloud mourns them both very greatly. It's really tough to say which one he would mourn more, though, and which one I would mourn more if I were in his place. He knew Zack longer and the two of them became really good friends. Zack kind of seemed to take on an older brother role of sorts for Cloud, and basically was to Cloud what Angeal was to him. Then on the other hand, he became friends with Aerith just as quickly as he had Zack, and also he took the role of her bodyguard very seriously. Even after the initial clash with the Turks that was really the only thing he was asked to save her from, he took it to heart that he always had to protect her, because that's simply what Cloud does. He's demonstrated such behavior before regarding his promise to Tifa and his inability to not be able to save her from falling off that cliff when they were children and then rushing to her side in the reactor at Nibelheim.
I never got the impression that Cloud blamed himself for Zack's death, though. Protecting Zack was never Cloud's responsibility. Indeed, Zack was a first class SOLDIER and often times was the one looking after and protecting Cloud. Of course that in itself was probably guilt enough, maybe he thinks that Zack would have lived had he not been there to slow him down.
But yes, as I said earlier in the post Cloud did consider protecting Aerith to be his responsibility and he feels that his ineptitude at his job is what caused her death. Let's just be glad that Tifa didn't also die as well. As tough as she is and as much as she can probably take care of herself there's still the promise at the well and Cloud would probably feel that protecting Tifa was another one of his failed responsibilities.
Poor dude needs to sop being so hard on himself.
