I believe that the biggest difference between the 2 is that Dazai was turned into the way he was while Fyodor just had a god complex since he was born.
If you didn't know yet, Dazai was molded into the way he was in the PM by Mori who had seen his intelligence and wanted Dazai to work for him, so he was trained at a very young age. But because he was molded the way he was, he still had shreds of feeling left and it could be seen by his 2 friends during the PM: Ango and Oda, and those two were the ones that really mattered to him. So when he lost them, he would have normally just completely gone crazy like Fyodor. But because Oda knew that and didn't want him to turn out that way, his dying last words were for him to be a good person. And because Dazai cared about them above anything else, he immediately quit the PM and was picked up by Fukuzawa. And since then, he has tried to surround himself with friends; friends like Ango and Oda were once to him and that had a major change to his mentality. And having experienced both sides of the world and with the request of Oda, he started to protect the good in the world by any means possible, which was why he took in Atsushi.
On the other hand, Fyodor was born the way he was. And because of his ability "Crime and Punishment" which can kill anyone with a touch, he was most likely isolated from his peers and thus never had a connection as Dazai did. And Fyodor becomes much more self-centered and his personality just keeps becoming worse with no one to keep him in check. And his ideals become much darker as he sees anyone that isn't as smart as him as worthless and isn't worth protecting. And with no guidance, he sought power above anything else; absolute power with no one to oppose him, and that naturally made Dazai his natural enemy. Not only is Dazai just as smart as him, but also his ability "No Longer Human" was the very thing standing in his way.
(This is just my theory as we don't completely know Fyodor's ability or his past yet)