Quite possibly neither.
Killing someone is not necessarily murder. Murder is a human killing another human without a legally justifiable reason. It's a question of whether or not the kill was lawful. I'll assume that for this hypothetical my killing of Evil Tautology occurs where a human government has legal jurisdiction.
It can't be suicide; the killing of oneself. No matter how like me this person is they are still not me. I am myself and no one else can truly be me. Unless killing him causes me to die as well, then it's suicide.
We should not forget that Evil Tautology is also evil and thus has no qualms about killing me himself. If we were to meet, he would likely attack me unprovoked. My retaliation and subsequent killing of him would be ruled justifiable homicide or manslaughter. Neither is murder. It's called self defense.
The universe the event occurs in may also factor into my defense. The universe my evil double hails from is itself defined as being evil, I doubt they would have a legal concept of murder. Hell, they might view my actions as being lawful by their standards. If it happens in my own universe, I could probably argue that because he was from an evil universe his intentions here were malicious and I killed him in order to protect everyone else. This would be a justifiable homicide.
If I took him to another universe and killed him there, depending on their laws, it could be murder. Unless there's a Multiverse Legal Code binding all universes. At that point I'm inside Jet Li's The One, it's definitely murder, and I'm being pursued by Coptology!