Well the easy answer would be to use whichever one works best. Even if a wired connection would be faster if it doesn't work well it then it doesn't do you any good. What is interesting is WHY the wired connection would be worse, as that SHOULD be the more stable of the two. Directly wiring into stuff is always the best choice if you are within range to do it.
What type of connection are we talking about (DSL, Cable ?)
And how exactly does the apartment have both wired and wireless? Where is the wireless coming from is what i am getting at, some sort of hot spots around your apt. complex?